### All GRE Math Resources

## Example Questions

### 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:**

**Correct answer:**18

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

### Example Question #2 : 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:**

inches

foot

foot

inches

foot

**Correct answer:**

inches

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 : Acute / Obtuse Isosceles 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:**

To solve this problem apply the formula: .

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

Thus, the solution is:

### Example Question #3 : Acute / Obtuse Isosceles Triangles

Find the perimeter of the acute Isosceles triangle shown above.

**Possible Answers:**

**Correct answer:**

To solve this problem apply the formula: .

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

### Example Question #4 : Acute / Obtuse 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

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 #5 : Acute / Obtuse Isosceles Triangles

Find the perimeter of the acute Isosceles triangle shown above.

**Possible Answers:**

**Correct answer:**

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 #6 : Acute / Obtuse Isosceles Triangles

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

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 #7 : Acute / Obtuse Isosceles Triangles

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

feet

inches

feet

inches

**Correct answer:**

inches

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 #8 : Acute / Obtuse Isosceles 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:**

foot

inches

inches

foot

foot

**Correct answer:**

inches

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 #9 : Acute / Obtuse Isosceles 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

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.