# GRE Math : Acute / Obtuse Isosceles Triangles

## 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?

18
12
32
14
20
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?

foot

foot

inches

foot

inches

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 #53 : Geometry

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?

Explanation:

To solve this problem apply the formula: .

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

Thus, the solution is:

### Example Question #54 : Geometry

Find the perimeter of the acute Isosceles triangle shown above.

Explanation:

To solve this problem apply the formula: .

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

### Example Question #55 : Geometry

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?

ft

ft

ft

ft

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 #56 : Geometry

Find the perimeter of the acute Isosceles triangle shown above.

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 : How To Find The Perimeter Of An Acute / Obtuse Isosceles Triangle

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?

inches

inches

inches

inches

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 : How To Find The Perimeter Of An Acute / Obtuse Isosceles Triangle

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?

feet

feet

inches

inches

inches

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 #1 : How To Find The Perimeter Of An Acute / Obtuse Isosceles Triangle

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?

foot

foot

foot

inches

inches

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 : How To Find The Perimeter Of An Acute / Obtuse Isosceles Triangle

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.

inches

inches

inches

inches

inches

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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