GRE Math : How to find the perimeter of an acute / obtuse isosceles triangle

Study concepts, example questions & explanations for GRE Math

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Example Questions

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Example Question #1 : Triangles

What is the perimeter of an isosceles triangle given that the sides 5 units long and half of the base measures to 4 units?

Possible Answers:
18
12
14
32
20
Correct answer: 18
Explanation:

The base of the triangle is 4 + 4 = 8 so the total perimeter is 5 + 5 + 8 = 18.

Example Question #1 : Isosceles Triangles

An acute Isosceles triangle has two sides with length  and one side length . The length of side   ft. If the length of  half the length of side , what is the perimeter of the triangle? 

Possible Answers:

 foot

 inches

 foot

 foot

 inches

Correct answer:

 inches

Explanation:

This Isosceles triangle has two sides with a length of  foot and one side length that is half of the length of the two equivalent sides. 

To find the missing side, double the value of side 's denominator:

. Thus, half of .

Therefore, this triangle has two sides with lengths of  and one side length of 

To find the perimeter, apply the formula: 





 foot  inches


Example Question #2 : Triangles

An acute Isosceles triangle has two sides with length  and one side length . The length of side  . If the length of  half the length of side , what is the perimeter of the triangle? 

Possible Answers:

Correct answer:

Explanation:

To solve this problem apply the formula: .

However, first calculate the length of the missing side by: .

Thus, the solution is:

Example Question #3 : Triangles

Isos._cont._gre

Find the perimeter of the acute Isosceles triangle shown above. 

Possible Answers:

Correct answer:

Explanation:

To solve this problem apply the formula: .

However, first calculate the length of the missing side by:







Example Question #3 : Isosceles Triangles

An obtuse Isosceles triangle has two sides with length  and one side length . The length of side   ft. If the length of  half the length of side , what is the perimeter of the triangle? 

Possible Answers:

 ft

 ft

 ft

 ft

Correct answer:

 ft

Explanation:

By definition, an Isosceles triangle must have two equivalent side lengths. Since we are told that  ft and that the sides with length  are half the length of side , find the length of  by:  and half of . Thus, both of sides with length  must equal  ft. 

Now, apply the formula: .



Then, simplify the fraction/convert to mixed number fraction:



 

Example Question #4 : Triangles

Isos._cont._gre

Find the perimeter of the acute Isosceles triangle shown above. 

Possible Answers:

Correct answer:

Explanation:

In order to solve this problem, first find the length of the missing sides. Then apply the formula: 

Each of the missing sides equal: 

 

Then apply the perimeter formula:

Example Question #1 : Triangles

Isos._gre_series_

An acute Isosceles triangle has two sides with length  and one side length . The length of side   inches. If the length of  , what is the perimeter of the triangle? 

Possible Answers:

 inches

 inches

 inches

 inches

Correct answer:

 inches

Explanation:

In order to solve this problem, first find the length of the missing sides. Then apply the formula: 

The missing side equals:



Then plug each side length into the perimeter formula:



 

Example Question #2 : Triangles

Isos._gre_series_

An acute Isosceles triangle has two sides with length  and one side length . The length of side   inches. If the length of , what is the perimeter of the triangle?

Possible Answers:

 inches

 inches

 feet

 feet

 inches

Correct answer:

 inches

Explanation:

In order to solve this problem, first find the length of the missing sides. Then apply the formula: 

The missing side equals:





Then, apply the perimeter formula by plugging in the side values: 

Example Question #7 : Triangles

An acute Isosceles triangle has two sides with length  and one side length . The length of side   ft. If the length of   , what is the perimeter of the triangle? 

Possible Answers:

 inches 

 foot

 foot

 inches

 foot

Correct answer:

 inches 

Explanation:

To solve this problem apply the formula: .

However, first calculate the length of the missing side by:

 , Note that 




Since, it takes  inches to make one foot, the perimeter is equal to  inches. 

Example Question #4 : Triangles

An acute Isosceles triangle has two sides with length  and one side length . The length of side   inches. The length of side  . Find the perimeter of the triangle.

Possible Answers:

 inches

 inches

 inches

 inches

 inches

Correct answer:

 inches

Explanation:

To find the perimeter of this triangle, apply the formula: 









Note: Since this is an acute Isosceles triangle, the length of the base must be smaller than the length of both of the equivalent sides. 

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