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Intermediate Geometry : Triangles

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

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Example Question #13 : How To Find The Perimeter Of An Acute / Obtuse Triangle

In terms of , find the perimeter.

Possible Answers:

$6x+2x\sqrt3$

$8x+2x\sqrt3$

$4x+2x\sqrt3$

$2x+2x\sqrt3$

Correct answer:

$4x+2x\sqrt3$

Explanation:

Draw in the height to create a right triangle.

Now, using the relationship between the lengths of sides in a 30-60-90 triangle, we can find out that the height of the triangle is and the hypotenuse is .

The ratio of the sides in a 30-60-90 triangle are: $x:x\sqrt3:2x$ .

The dashes on two sides of the triangle indicate that these two sides are congruent. The three side lengths of the triangle are $2x, 2x, \text{ and }2x\sqrt3$ .

Now, add up these side lengths to find the perimeter.

$\text{Perimeter}=2x+2x+2x\sqrt3=4x+2x\sqrt3$

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Example Question #14 : How To Find The Perimeter Of An Acute / Obtuse Triangle

In terms of , find the perimeter.

Possible Answers:

$62x+42x\sqrt3$

$84x+42x\sqrt3$

$42x+42x\sqrt3$

$84+42x\sqrt3$

Correct answer:

$84x+42x\sqrt3$

Explanation:

Draw in the height to create a right triangle.

Now, using the relationship between the lengths of sides in a 30-60-90 triangle, we can find out that the height of the triangle is 21x and the hypotenuse is 42x .

The ratio of the sides in a 30-60-90 triangle are: $x:x\sqrt3:2x$ .

The dashes on two sides of the triangle indicate that these two sides are congruent. The three side lengths of the triangle are $42x, 42x, \text{ and }42x\sqrt3$ .

Now, add up these side lengths to find the perimeter.

$\text{Perimeter}=42x+42x+42x\sqrt3=84x+42x\sqrt3$

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Example Question #15 : How To Find The Perimeter Of An Acute / Obtuse Triangle

Find the perimeter of the triangle below. Round to the nearest tenths place.

Possible Answers:

59.1

59.7

58.3

47.8

Correct answer:

59.7

Explanation:

Draw in the height to create a right triangle.

Now, using the relationship between the lengths of sides in a 30-60-90 triangle, we can find out that the height of the triangle is and the hypotenuse is .

The ratio of the sides in a 30-60-90 triangle are: $x:x\sqrt3:2x$ .

The dashes on two sides of the triangle indicate that these two sides are congruent. The three side lengths of the triangle are $16, 16, \text{ and }16\sqrt3$ .

Now, add up these side lengths to find the perimeter.

$\text{Perimeter}=16+16+16\sqrt3=59.7$

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Example Question #16 : How To Find The Perimeter Of An Acute / Obtuse Triangle

In terms of , find the perimeter of the triangle.

Possible Answers:

$72x+36x\sqrt3$

$36x+36x\sqrt3$

$72+36x\sqrt3$

$108x+36x\sqrt3$

Correct answer:

$72x+36x\sqrt3$

Explanation:

Draw in the height to create a right triangle.

Now, using the relationship between the lengths of sides in a 30-60-90 triangle, we can find out that the height of the triangle is 18x and the hypotenuse is 36x .

The ratio of the sides in a 30-60-90 triangle are: $x:x\sqrt3:2x$ .

The dashes on two sides of the triangle indicate that these two sides are congruent. The three side lengths of the triangle are $36x, 36x, \text{ and }36x\sqrt3$ .

Now, add up these side lengths to find the perimeter.

$\text{Perimeter}=36x+36x+36x\sqrt3=72x+36x\sqrt3$

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Example Question #17 : How To Find The Perimeter Of An Acute / Obtuse Triangle

A triangle is defined by the following points on a coordinate plane: (1, 5), (2, 12), (-3, 4)

What is the perimeter of the triangle?

Possible Answers:

22.49

21.67

20.63

25.06

Correct answer:

20.63

Explanation:

In order to find the perimeter of the triangle, we will first need to find the length of each side of the triangle by using the distance formula.

Recall the distance formula for a line:

$\text{distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

The first side of the triangle is the line segment made with $(1, 5)\text{ and }(2, 12)$ as its endpoints.

$\text{side 1}=\sqrt{(2-1)^2+(12-5)^2}=\sqrt{50}=5\sqrt2$

The second side of the triangle is the line segment that has $(2, 12)\text{ and }(-3, 4)$ as its endpoints.

$\text{side 2}=\sqrt{(2-(-3))^2+(12-4)^2}=\sqrt{89}$

The third side of the triangle is the line segment that has $(-3, 4)\text{ and }(1, 5)$ as its endpoints.

$\text{side 3}=\sqrt{(1-(-3))^2+(5-4)^2}=\sqrt{17}$

Now, add up these three sides with a calculator to find the perimeter of the triangle.

$\text{Perimeter}=5\sqrt{2} +\sqrt{89}+\sqrt{17}=20.63$

Make sure to round to places after the decimal.

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Example Question #18 : How To Find The Perimeter Of An Acute / Obtuse Triangle

A triangle is defined by the following points in a coordinate plane: (5, 6), (7, 2), (9, 11) .

What is the perimeter of the triangle?

Possible Answers:

22.13

24.59

26.78

20.09

Correct answer:

20.09

Explanation:

In order to find the perimeter of the triangle, we will first need to find the length of each side of the triangle by using the distance formula.

Recall the distance formula for a line:

$\text{distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

The first side of the triangle is the line segment made with $(5, 6)\text{ and }(7, 2)$ as its endpoints.

$\text{side 1}=\sqrt{(7-5)^2+(2-6)^2}=\sqrt{20}=2\sqrt5$

The second side of the triangle is the line segment that has $(7, 2)\text{ and }(9, 11)$ as its endpoints.

$\text{side 2}=\sqrt{(9-7)^2+(11-2)^2}=\sqrt{85}$

The third side of the triangle is the line segment that has $(5, 6)\text{ and }(9, 11)$ as its endpoints.

$\text{side 3}=\sqrt{(9-5)^2+(11-6)^2}=\sqrt{41}$

Now, add up these three sides with a calculator to find the perimeter of the triangle.

$\text{Perimeter}=2\sqrt{5} +\sqrt{85}+\sqrt{41}=20.09$

Make sure to round to places after the decimal.

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Example Question #19 : How To Find The Perimeter Of An Acute / Obtuse Triangle

A triangle is defined by the following points on a coordinate plane: (-5, 1), (6, -2), (7, 0) .

What is the perimeter of the triangle?

Possible Answers:

30.01

27.09

28.81

25.68

Correct answer:

25.68

Explanation:

In order to find the perimeter of the triangle, we will first need to find the length of each side of the triangle by using the distance formula.

Recall the distance formula for a line:

$\text{distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

The first side of the triangle is the line segment made with $(-5, 1)\text{ and }(6, -2)$ as its endpoints.

$\text{side 1}=\sqrt{(6-(-5))^2+(-2-1)^2}=\sqrt{130}$

The second side of the triangle is the line segment that has $(6, -2)\text{ and }(7, 0)$ as its endpoints.

$\text{side 2}=\sqrt{(7-6)^2+(0-(-2))^2}=\sqrt{5}$

The third side of the triangle is the line segment that has $(-5, 1)\text{ and }(7, 0)$ as its endpoints.

$\text{side 3}=\sqrt{(7-(-5))^2+(0-1)^2}=\sqrt{145}$

Now, add up these three sides with a calculator to find the perimeter of the triangle.

$\text{Perimeter}=\sqrt{130} +\sqrt{5}+\sqrt{145}=25.68$

Make sure to round to places after the decimal.

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Example Question #20 : How To Find The Perimeter Of An Acute / Obtuse Triangle

A triangle is defined by the following points on a coordinate plane: (9, 8), (12, 0), (-1, -2) .

What is the perimeter of the triangle?

Possible Answers:

31.45

35.84

33.87

36.09

Correct answer:

35.84

Explanation:

In order to find the perimeter of the triangle, we will first need to find the length of each side of the triangle by using the distance formula.

Recall the distance formula for a line:

$\text{distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

The first side of the triangle is the line segment made with $(9, 8)\text{ and }(12, 0)$ as its endpoints.

$\text{side 1}=\sqrt{(12-9)^2+(0-8)^2}=\sqrt{73}$

The second side of the triangle is the line segment that has $(12, 0)\text{ and }(-1, -2)$ as its endpoints.

$\text{side 2}=\sqrt{(-1-12)^2+(-2-0)^2}=\sqrt{173}$

The third side of the triangle is the line segment that has $(9, 8)\text{ and }(-1, -2)$ as its endpoints.

$\text{side 3}=\sqrt{(-1-9))^2+(-2-8)^2}=\sqrt{200}=10\sqrt2$

Now, add up these three sides with a calculator to find the perimeter of the triangle.

$\text{Perimeter}=\sqrt{73} +\sqrt{173}+10\sqrt{2}=35.84$

Make sure to round to places after the decimal.

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Example Question #521 : Plane Geometry

A triangle is defined by the following points on a coordinate plane: (1, 1), (0, 5), (-9, -1) .

What is the perimeter of the triangle?

Possible Answers:

25.14

24.59

21.66

23.08

Correct answer:

25.14

Explanation:

In order to find the perimeter of the triangle, we will first need to find the length of each side of the triangle by using the distance formula.

Recall the distance formula for a line:

$\text{distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

The first side of the triangle is the line segment made with $(1, 1)\text{ and }(0, 5)$ as its endpoints.

$\text{side 1}=\sqrt{(0-1)^2+(5-1)^2}=\sqrt{17}$

The second side of the triangle is the line segment that has $(0, 5)\text{ and }(-9, -1)$ as its endpoints.

$\text{side 2}=\sqrt{(-9-0)^2+(-1-5)^2}=\sqrt{117}$

The third side of the triangle is the line segment that has $(1, 1)\text{ and }(-9,-1)$ as its endpoints.

$\text{side 3}=\sqrt{(-9-1)^2+(-1-1)^2}=\sqrt{104}$

Now, add up these three sides with a calculator to find the perimeter of the triangle.

$\text{Perimeter}=\sqrt{17} +\sqrt{117}+\sqrt{104}=25.14$

Make sure to round to places after the decimal.

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Example Question #522 : Plane Geometry

A triangle is defined by the following points on a coordinate plane: (1, -2), (2, -5), (-3, -3) .

What is the perimeter of the triangle?

Possible Answers:

12.67

11.41

10.51

17.89

Correct answer:

12.67

Explanation:

In order to find the perimeter of the triangle, we will first need to find the length of each side of the triangle by using the distance formula.

Recall the distance formula for a line:

$\text{distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

The first side of the triangle is the line segment made with $(1, -2)\text{ and }(2, -5)$ as its endpoints.

$\text{side 1}=\sqrt{(2-1)^2+(-5-(-2))^2}=\sqrt{10}$

The second side of the triangle is the line segment that has $(2, -5)\text{ and }(-3, -3)$ as its endpoints.

$\text{side 2}=\sqrt{(-3-2)^2+(-3-(-5))^2}=\sqrt{29}$

The third side of the triangle is the line segment that has $(1, -2)\text{ and }(-3, -3)$ as its endpoints.

$\text{side 3}=\sqrt{(-3-1)^2+(-3-(-2))^2}=\sqrt{17}$

Now, add up these three sides with a calculator to find the perimeter of the triangle.

$\text{Perimeter}=\sqrt{10} +\sqrt{29}+\sqrt{17}=12.67$

Make sure to round to places after the decimal.

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Intermediate Geometry : Triangles

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #13 : How To Find The Perimeter Of An Acute / Obtuse Triangle

Example Question #14 : How To Find The Perimeter Of An Acute / Obtuse Triangle

Example Question #15 : How To Find The Perimeter Of An Acute / Obtuse Triangle

Example Question #16 : How To Find The Perimeter Of An Acute / Obtuse Triangle

Example Question #17 : How To Find The Perimeter Of An Acute / Obtuse Triangle

Example Question #18 : How To Find The Perimeter Of An Acute / Obtuse Triangle

Example Question #19 : How To Find The Perimeter Of An Acute / Obtuse Triangle

Example Question #20 : How To Find The Perimeter Of An Acute / Obtuse Triangle

Example Question #521 : Plane Geometry

Example Question #522 : Plane Geometry

All Intermediate Geometry Resources

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