How to find the perimeter of an acute / obtuse isosceles triangle - GRE Quantitative Reasoning

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

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

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?

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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}$

A triangle has two sides with length and one side length . The length of side $\frac{1}{4}$ yard. If the length of the length of side , what is the perimeter of the triangle?

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The first step to solving this problem is that we must find the length of length $\small a.$ Since, $\small a$ is $\small 2$ 4 the length of side $\small b$ , use the following steps:

$\small \small b=\frac{1}{4}$$
$\small a=\frac{1}{4}$\times2=\frac{1}{2}$$

Now, apply the formula: $\small p=2a+b$

$\small p=\frac{2}{4}$+\frac{2}{4}$+\frac{1}{4}$=\frac{5}{4}$$

An acute Isosceles triangle has two sides with length and one side length . The length of side $\small a=$ $\small $\frac{3}{9}$$ ft. If the length of $\small b=$ half the length of side $\small a$ , what is the perimeter of the triangle?

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This Isosceles triangle has two sides with a length of $\small $\frac{3}{9}$$ 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 $\small a$ 's denominator:

$\small $\frac{3}{9}$=\frac{1}{3}$$ . Thus, half of $\small $\frac{1}{3}$=\frac{1}{6}$$ .

Therefore, this triangle has two sides with lengths of $\small $\frac{1}{3}$$ and one side length of $\small $\frac{1}{6}$$ .

To find the perimeter, apply the formula:

$\small p=2a+b$

$\small p=\frac{1}{3}$+\frac{1}{3}$+\frac{1}{6}$$

$\small p=\frac{2}{6}$+\frac{2}{6}$+\frac{1}{6}$=\frac{5}{6}$=\frac{10}{12}$$ foot $\small = 10$ inches

An acute Isosceles triangle has two sides with length and one side length . The length of side $\small a=$ $\small 13$ . If the length of $\small b=$ half the length of side $\small a$ , what is the perimeter of the triangle?

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

However, first calculate the length of the missing side by: $\small 13\div2=6.5$ .

Thus, the solution is:

$\small p=13+13+6.5=32.5$

Find the perimeter of the acute Isosceles triangle shown above.

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

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

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

$\small a=12\times5=60$

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

$\small p=120+12=132$

Find the perimeter of the acute Isosceles triangle shown above.

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In order to solve this problem, first find the length of the missing sides. Then apply the formula: $\small p=2a+b$

Each of the missing sides equal:

$\small a=\frac{7}{3}$\times4=\frac{28}{3}$$

Then apply the perimeter formula:
$\small p=\frac{28}{3}$+\frac{28}{3}$+\frac{7}{3}$=\frac{63}{3}$=21$

An acute Isosceles triangle has two sides with length and one side length . The length of side $\small a=$ inches. If the length of $\small b=$ $\sqrt[3]{a}$ , what is the perimeter of the triangle?

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In order to solve this problem, first find the length of the missing sides. Then apply the formula: $\small p=2a+b$

The missing side equals:

$b=\sqrt[3]{a}=\sqrt[3]{8}=2$

Then plug each side length into the perimeter formula:

An acute Isosceles triangle has two sides with length and one side length . The length of side $\small a=$ $\sqrt{144}$ inches. If the length of $\small b=a\times $\frac{1}{2}$$ , what is the perimeter of the triangle?

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In order to solve this problem, first find the length of the missing sides. Then apply the formula: $\small p=2a+b$

The missing side equals:

$\small a=$\sqrt{144}$=12$

$\small b=12\times $\frac{1}{2}$=\frac{12}{2}$=6$

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

$\small p=2(12)+6=24+6=30$

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.

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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 acute Isosceles triangle has two sides with length and one side length . The length of side $\small a=$ $\small \small $\frac{3}{12}$$ ft. If the length of $\small b=\small a\times $\frac{1}{3}$$ , what is the perimeter of the triangle?

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

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

$\small $\frac{3}{12}$+\frac{3}{12}$+($\frac{3}{12}$\times$\frac{1}{3}$)$ , Note that $\small $\frac{3}{36}$=\frac{1}{12}$$

$\small \small $\frac{6}{12}$+\frac{3}{36}$=\frac{6}{12}$+\frac{1}{12}$=\frac{7}{12}$$ .

Since, it takes $\small 12$ inches to make one foot, the perimeter is equal to $\small 7$ inches.

An acute Isosceles triangle has two sides with length and one side length . The length of side $\small a=$ $\small 8$ inches. The length of side $\small b=$ $\small a\times $\frac{1}{4}$$ . Find the perimeter of the triangle.

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

$\small p=2a+b$

$\small p=2(8)+(8\times $\frac{1}{4}$)$

$\small p=16+\frac{8}{4}$$

$\small p=16+2=18$

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.

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

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

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?

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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}$

A triangle has two sides with length and one side length . The length of side $\frac{1}{4}$ yard. If the length of the length of side , what is the perimeter of the triangle?

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The first step to solving this problem is that we must find the length of length $\small a.$ Since, $\small a$ is $\small 2$ 4 the length of side $\small b$ , use the following steps:

$\small \small b=\frac{1}{4}$$
$\small a=\frac{1}{4}$\times2=\frac{1}{2}$$

Now, apply the formula: $\small p=2a+b$

$\small p=\frac{2}{4}$+\frac{2}{4}$+\frac{1}{4}$=\frac{5}{4}$$

An acute Isosceles triangle has two sides with length and one side length . The length of side $\small a=$ $\small $\frac{3}{9}$$ ft. If the length of $\small b=$ half the length of side $\small a$ , what is the perimeter of the triangle?

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This Isosceles triangle has two sides with a length of $\small $\frac{3}{9}$$ 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 $\small a$ 's denominator:

$\small $\frac{3}{9}$=\frac{1}{3}$$ . Thus, half of $\small $\frac{1}{3}$=\frac{1}{6}$$ .

Therefore, this triangle has two sides with lengths of $\small $\frac{1}{3}$$ and one side length of $\small $\frac{1}{6}$$ .

To find the perimeter, apply the formula:

$\small p=2a+b$

$\small p=\frac{1}{3}$+\frac{1}{3}$+\frac{1}{6}$$

$\small p=\frac{2}{6}$+\frac{2}{6}$+\frac{1}{6}$=\frac{5}{6}$=\frac{10}{12}$$ foot $\small = 10$ inches

An acute Isosceles triangle has two sides with length and one side length . The length of side $\small a=$ $\small 13$ . If the length of $\small b=$ half the length of side $\small a$ , what is the perimeter of the triangle?

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

However, first calculate the length of the missing side by: $\small 13\div2=6.5$ .

Thus, the solution is:

$\small p=13+13+6.5=32.5$

Find the perimeter of the acute Isosceles triangle shown above.

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

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

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

$\small a=12\times5=60$

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

$\small p=120+12=132$

Find the perimeter of the acute Isosceles triangle shown above.

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In order to solve this problem, first find the length of the missing sides. Then apply the formula: $\small p=2a+b$

Each of the missing sides equal:

$\small a=\frac{7}{3}$\times4=\frac{28}{3}$$

Then apply the perimeter formula:
$\small p=\frac{28}{3}$+\frac{28}{3}$+\frac{7}{3}$=\frac{63}{3}$=21$

An acute Isosceles triangle has two sides with length and one side length . The length of side $\small a=$ inches. If the length of $\small b=$ $\sqrt[3]{a}$ , what is the perimeter of the triangle?

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In order to solve this problem, first find the length of the missing sides. Then apply the formula: $\small p=2a+b$

The missing side equals:

$b=\sqrt[3]{a}=\sqrt[3]{8}=2$

Then plug each side length into the perimeter formula: