ISEE Middle Level Math : Triangles

Study concepts, example questions & explanations for ISEE Middle Level Math

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Example Questions

Example Question #21 : Plane Geometry

Use the following image to answer the question:

Triangle6

Find the perimeter of the triangle.

Possible Answers:

\displaystyle 36\text{ft}

\displaystyle 72\text{ft}

\displaystyle 28\text{ft}

\displaystyle 18\text{ft}

\displaystyle 16\text{ft}

Correct answer:

\displaystyle 28\text{ft}

Explanation:

To find the perimeter of a triangle, we will use the following formula:

\displaystyle \text{perimeter of triangle} = a+b+c

where a, b, and c are the lengths of the sides of the triangle.

 

Now, let's look at the triangle.

Triangle6

We can see the triangle has sides with lengths of 10 feet, 6 feet, and 12 feet.

Knowing this, we can substitute into the formula.  We get

\displaystyle \text{perimeter of triangle} = 10\text{ft} + 6\text{ft} +12\text{ft}

\displaystyle \text{perimeter of triangle} = 28\text{ft}

Example Question #22 : Plane Geometry

Find the perimeter of an equilateral triangle that has a base of 10 feet.

Possible Answers:

\displaystyle 50\text{ft}

\displaystyle 100\text{ft}

\displaystyle 20\text{ft}

\displaystyle \text{There is not enough information to solve the problem.}

\displaystyle 30\text{ft}

Correct answer:

\displaystyle 30\text{ft}

Explanation:

To find the perimeter of a triangle, we will use the following formula:

\displaystyle \text{perimeter of triangle} = a+b+c

where a, b, and c are the lengths of the sides of the triangle.

 

Now, we know the base of the triangle is 10 feet.  Because it is an equilateral triangle, we know that all sides are equal.  Therefore, all sides are 10 feet.  

Knowing this, we can substitute into the formula.  We get

\displaystyle \text{perimeter of triangle} = 10\text{ft} +10\text{ft} +10\text{ft}

\displaystyle \text{perimeter of triangle} = 30\text{ft}

Example Question #23 : Plane Geometry

Find the perimeter of an equilateral triangle with a base of 6ft.

Possible Answers:

\displaystyle 36\text{ft}

\displaystyle 18\text{ft}

\displaystyle \text{There is not enough information to solve the problem.}

\displaystyle 12\text{ft}

\displaystyle 24\text{ft}

Correct answer:

\displaystyle 18\text{ft}

Explanation:

To find the perimeter of a triangle, we will use the following formula:

\displaystyle \text{perimeter of triangle} = a+b+c

where a, b, and are the lengths of the sides of the triangle.

 

Now, we know the base of the triangle is 6ft.  Because it is an equilateral triangle, we know that all sides are equal.  Therefore, all sides are 6ft. 

Knowing this, we can substitute into the formula.  We get

\displaystyle \text{perimeter of triangle} = 6\text{ft} + 6\text{ft} + 6\text{ft}

\displaystyle \text{perimeter of triangle} = 18\text{ft}

Example Question #24 : Plane Geometry

Find the perimeter of an equilateral triangle with a base of length 17in.

Possible Answers:

\displaystyle 34\text{in}

\displaystyle 51\text{in}

\displaystyle \text{There is not enough information to solve the problem.}

\displaystyle 28\text{in}

\displaystyle 47\text{in}

Correct answer:

\displaystyle 51\text{in}

Explanation:

To find the perimeter of a triangle, we will use the following formula:

\displaystyle \text{perimeter of triangle} = a+b+c

where a, b, and c are the lengths of the sides of the triangle.

 

Now, we know the base of the triangle has a length of 17in.  Because it is an equilateral triangle, all lengths are the same.  Therefore, all lengths are 17in.

Knowing this, we can substitute into the formula.  We get

\displaystyle \text{perimeter of triangle} = 17\text{in} +17\text{in} +17\text{in}

\displaystyle \text{perimeter of triangle} = 51\text{in}

Example Question #25 : Plane Geometry

Find the perimeter of an equilateral triangle with a base of 14cm.

Possible Answers:

\displaystyle 42\text{cm}

\displaystyle 27\text{cm}

\displaystyle 18\text{cm}

\displaystyle 36\text{cm}

\displaystyle 21\text{cm}

Correct answer:

\displaystyle 42\text{cm}

Explanation:

To find the perimeter of a triangle, we will use the following formula:

\displaystyle \text{perimeter of triangle} = a+b+c

where a, b, and c are the lengths of the sides of the triangle.

 

Now, we know the base of the triangle is 14cm.  Because it is an equilateral triangle, all sides are equal.  Therefore, all sides are 14cm.

Knowing this, we can substitute into the formula.  We get

\displaystyle \text{perimeter of triangle} = 14\text{cm} +14\text{cm} +14\text{cm}

\displaystyle \text{perimeter of triangle} = 42\text{cm}

Example Question #26 : Plane Geometry

Find the perimeter of an equilateral triangle with a base of length 34in.

Possible Answers:

\displaystyle 76\text{in}

\displaystyle 51\text{in}

\displaystyle 94\text{in}

\displaystyle 102\text{in}

\displaystyle 68\text{in}

Correct answer:

\displaystyle 102\text{in}

Explanation:

To find the perimeter of a triangle, we will use the following formula:

\displaystyle P = a+b+c

where a, b, and c are the lengths of the sides of the triangle.

 

Now, we know the base of the triangle is 34in.  Because it is an equilateral triangle, all sides are equal.  Therefore, all sides are 34in.

Knowing this, we can substitute into the formula.  We get

\displaystyle P = 34\text{in} + 34\text{in} +34\text{in}

\displaystyle P = 102\text{in}

Example Question #27 : Plane Geometry

Find the perimeter of a triangle that has a base of 16in.

Possible Answers:

\displaystyle 108\text{in}

\displaystyle 48\text{in}

\displaystyle 128\text{in}

\displaystyle 24\text{in}

\displaystyle 32\text{in}

Correct answer:

\displaystyle 48\text{in}

Explanation:

To find the perimeter of a triangle, we will use the following formula:

\displaystyle P = a+b+c

where a, b, and c are the lengths of the sides of the triangle.

 

Now, we know the base of the triangle is 16in.  Because it is an equilateral triangle, all sides are equal.  Therefore, all sides are 16in.

Knowing this, we will substitute into the formula.  We get

\displaystyle P = 16\text{in} + 16\text{in} + 16\text{in}

\displaystyle P = 48\text{in}

Example Question #28 : Plane Geometry

Use the following triangle to answer the question:

Triangle7

Find the perimeter.

Possible Answers:

\displaystyle 24\text{cm}

\displaystyle 48\text{cm}

\displaystyle 14\text{cm}

\displaystyle 18\text{cm}

\displaystyle 32\text{cm}

Correct answer:

\displaystyle 18\text{cm}

Explanation:

To find the perimeter of a triangle, we will use the following formula:

\displaystyle P = a+b+c

where a, b, and c are the lengths of the sides of the triangle.

 

Now, given the triangle,

Triangle7

we can see it has sides with length 8cm, 4cm, and 6cm.  Knowing this, we can substitute into the formula.  We get

\displaystyle P = 8\text{cm} +4\text{cm} + 6\text{cm}

\displaystyle P=18\text{cm}

Example Question #29 : Plane Geometry

The perimeter of an equilateral triangle is 39cm.  Find the length of one side.

Possible Answers:

\displaystyle 13\text{cm}

\displaystyle 12\text{cm}

\displaystyle \text{There is not enough information to answer the question.}

\displaystyle 11\text{cm}

\displaystyle 14\text{cm}

Correct answer:

\displaystyle 13\text{cm}

Explanation:

To find the perimeter of an equilateral triangle, we use this formula

\displaystyle P = 3a

where a is the length of one side.  An equilateral triangle has 3 equal sides.  That is why we multiply the length of one side by 3.  To find the length of one side, we will solve for a.

 

Now, we know the perimeter of the equilateral triangle is 39cm.  So, we can substitute.  We get

 

\displaystyle 39\text{cm} = 3a

 

\displaystyle \frac{39\text{cm}}{3} = \frac{3a}{3}

 

\displaystyle 13\text{cm} = a

 

\displaystyle a=13\text{cm}

 

Therefore, the length of one side of the equilateral triangle is 13cm.

Example Question #30 : Plane Geometry

Find the perimeter of an equilateral triangle with a base of 14in.

Possible Answers:

\displaystyle 48\text{in}

\displaystyle \text{There is not enough information to solve the problem.}

\displaystyle 28\text{in}

\displaystyle 42\text{in}

\displaystyle 36\text{in}

Correct answer:

\displaystyle 42\text{in}

Explanation:

To find the perimeter of a triangle, we will use the following formula:

\displaystyle P = a+b+c

where a, b, and c are the lengths of the sides of the triangle.

 

Now, we know the base of the triangle is 14in.  Because it is an equilateral triangle, all sides are equal.  Therefore, all sides are 14in.  So, we can substitute.

\displaystyle P = 14\text{in} + 14\text{in} + 14\text{in}

\displaystyle P = 42\text{in}

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