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Intermediate Geometry : How to find the perimeter of an acute / obtuse triangle

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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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Example Question #523 : Plane Geometry

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

What is the perimeter of the triangle?

Possible Answers:

11.44

12.09

8.55

9.14

Correct answer:

9.14

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 $(-1, -1)\text{ and }(-2, -2)$ as its endpoints.

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

The second side of the triangle is the line segment that has $(-2, -2)\text{ and }(-5, 0)$ as its endpoints.

$\text{side 2}=\sqrt{(-5-(-2))^2+(0-(-2))^2}=\sqrt{13}$

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

$\text{side 3}=\sqrt{(-5-(-1))^2+(0-(-1))^2}=\sqrt{17}$

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

$\text{Perimeter}=\sqrt{2} +\sqrt{13}+\sqrt{17}=9.14$

Make sure to round to places after the decimal.

Report an Error

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Intermediate Geometry : How to find the perimeter of an acute / obtuse triangle

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #521 : Plane Geometry

Example Question #522 : Plane Geometry

Example Question #523 : Plane Geometry

All Intermediate Geometry Resources

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