How to find the height of a right triangle - SSAT Upper Level Quantitative (Math)

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Question

If the hypotenuse of a right triangle is 20, and one of the legs is 12, what is the value of the other leg?

Answer

The triangle in this problem is a variation of the 3, 4, 5 right triangle. However, it is 4 times bigger. We know this because $5\cdot4=20$ (the length of the hypotenuse) and $3\cdot4=12$ (the length of one of the legs).

Therefore, the length of the other leg will be equal to:

$4\cdot4=16$

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Question

A given right triangle has a base of length and a total area of $45cm^{2}$ . What is the height of the right triangle?

Answer

For a given right triangle with base and height , the area can be defined by the formula $A=\frac{1}{2}bh$ . If one leg of the right triangle is taken as the base, then the other leg is the height.

Therefore, to find the height , we restructure the formula for the area as follows:

$A=\frac{1}{2}bh$

$\frac{2A}{b}=h$

Plugging in our values for and :

$\frac{2(45cm^{2})}{9cm}=h$

$\frac{90cm^{2}}{9cm}=h$

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Question

A given right triangle has a base length of and a total area of $100cm^{2}$ . What is the height of the triangle?

Answer

For a given right triangle with base and height , the area can be defined by the formula $A=\frac{1}{2}bh$ . If one leg of the right triangle is taken as the base, then the other leg is the height.

Therefore, to find the height , we restructure the formula for the area as follows:

$A=\frac{1}{2}bh$

$\frac{2A}{b}=h$

Plugging in our values for and :

$\frac{2(100cm^{2})}{10cm}=h$

$\frac{200cm^{2}}{10cm}=h$

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Question

A given right triangle has a hypotenuse of and a total area of $200cm^{2}$ . What is the height of the triangle?

Answer

For a given right triangle with base and height , the area can be defined by the formula $A=\frac{1}{2}bh$ . If one leg of the right triangle is taken as the base, then the other leg is the height.

However, we have not been given a base or leg length for the right triangle, only the length of the hypotenuse and the area. We therefore do not have enough information to solve for the height .

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Question

The area of a right triangle is $50\textup{ in}^2$ . If the base of the triangle is $10\textup{ in}$ , what is the length of the height, in inches?

Answer

To find the height, plug what is given in the question into the formula used to find the area of a triangle.

$\text{Area}=\frac{base\times height}{2}$

Use the information given in the question:

$\text{Base}=10$

$\text{Area}=50$

$50=\frac{10\times height}{2}$

Now, solve for the height.

$10\times height=100$

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Question

The area of a right triangle is . If the base of the triangle is , what is the height, in meters?

Answer

To find the height, plug what is given in the question into the formula used to find the area of a triangle.

$\text{Area}=\frac{base\times height}{2}$

Use the information given in the question:

$\text{Base}=25$

$\text{Area}=100$

$100=\frac{25\times height}{2}$

Now, solve for the height.

$25\times height=200$

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Question

The area of a right triangle is , and the base is . What is the height, in meters?

Answer

To find the height, plug what is given in the question into the formula used to find the area of a triangle.

$\text{Area}=\frac{base\times height}{2}$

Use the information given in the question:

$\text{Base}=15$

$\text{Area}=45$

$45=\frac{15\times height}{2}$

Now, solve for the height.

$15\times height=90$

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