Acute / Obtuse Isosceles Triangles

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GRE Quantitative Reasoning › Acute / Obtuse Isosceles Triangles

Questions 1 - 10

An obtuse Isosceles triangle has two sides with length and one side length . The length of side $\frac{3}{4}$ ft. If the length of half the length of side , what is the perimeter of the triangle?

$1\frac{1}{2}$ ft

$\frac{12}{4}$ ft

$1\frac{2}{3}$ ft

$1\frac{1}{3}$ ft

Explanation

By definition, an Isosceles triangle must have two equivalent side lengths. Since we are told that $b=\frac{3}{4}$ ft and that the sides with length are half the length of side , find the length of by: $\frac{3}{4}=\frac{6}{8}$ and half of $\frac{6}{8}=\frac{3}{8}$ . Thus, both of sides with length must equal $\frac{3}{8}$ ft.

Now, apply the formula: .

$p=\frac{3}{8}+\frac{3}{8}+\frac{6}{8}=\frac{12}{8}$

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

$\frac{12}{8}=\frac{3}{2}=1\frac{1}{2}$

An obtuse Isosceles triangle has two sides with length and one side length . The length of side $\frac{3}{4}$ ft. If the length of half the length of side , what is the perimeter of the triangle?

$1\frac{1}{2}$ ft

$\frac{12}{4}$ ft

$1\frac{2}{3}$ ft

$1\frac{1}{3}$ ft

Explanation

Now, apply the formula: .

$p=\frac{3}{8}+\frac{3}{8}+\frac{6}{8}=\frac{12}{8}$

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

$\frac{12}{8}=\frac{3}{2}=1\frac{1}{2}$

Isos._cont._gre

Find the perimeter of the acute Isosceles triangle shown above.

$\small 132$

$\small 130$

$\small 133$

$\small 120$

$\small \small 60$

Explanation

To solve this problem apply the formula: $\small p=2a+b$ .

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

$\small p=2(a)+12$

$\small a=12\times5=60$

$\small p=2(60)+12$

$\small p=120+12=132$

Isos._cont._gre

Find the perimeter of the acute Isosceles triangle shown above.

$\small 132$

$\small 130$

$\small 133$

$\small 120$

$\small \small 60$

Explanation

To solve this problem apply the formula: $\small p=2a+b$ .

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

$\small p=2(a)+12$

$\small a=12\times5=60$

$\small p=2(60)+12$

$\small p=120+12=132$

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

Explanation

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

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

Explanation

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

Isos._cont._gre

The obtuse Isosceles triangle shown above has two sides with length and one side length . The length of side $\small a=$ $\small 43$ inches. Side length $\small b=2a$ . Find the perimeter of the triangle.

$\small 172$ inches

$\small 15\sqrt{2}$ inches

$\small 86$ inches

$\small 129$ inches

$\small 84$ inches

Explanation

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

$\small p=2a+b$

Since, $\small a=43$ , and $\small b=2a$ then $\small b$ must have a value of: $\small 2\times43=86$

This triangle has two side lengths of $\small 43$ inches, and one side length of $\small 86$ inches.

Thus, the solution is:

$\small p=2(43)+86=172$

Isos._cont._gre

$\small 172$ inches

$\small 15\sqrt{2}$ inches

$\small 86$ inches

$\small 129$ inches

$\small 84$ inches

Explanation

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

$\small p=2a+b$

Since, $\small a=43$ , and $\small b=2a$ then $\small b$ must have a value of: $\small 2\times43=86$

This triangle has two side lengths of $\small 43$ inches, and one side length of $\small 86$ inches.

Thus, the solution is:

$\small p=2(43)+86=172$

An isosceles triangle has one obtuse angle that is $112^{\circ}$ . What is the value of one of the other angles?

$34^{\circ}$

$68^{\circ}$

$90^{\circ}$

$112^{\circ}$

$45^{\circ}$

Explanation

We know that an isosceles triangel has two equal sides and thus two equal angles opposite those equal sides. Because there is one obtuse angle of 112 degrees we automatically know that this angle is the vertex. If you sum any triangle's interior angles, you always get 180 degrees.

180 – 112 = 68 degrees. Thus there are 68 degrees left for the two equal angles. Each angle must therefore measure 34 degrees.

Isosceles-triangle-1