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

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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?

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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 . What is the height of the right triangle?

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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 :

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Question

A given right triangle has a base length of and a total area of . What is the height of the triangle?

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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 :

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Question

A given right triangle has a hypotenuse of and a total area of . What is the height of the triangle?

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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?

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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?

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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?

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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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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?

Tap to reveal answer

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 . What is the height of the right triangle?

Tap to reveal answer

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 :

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Question

A given right triangle has a base length of and a total area of . What is the height of the triangle?

Tap to reveal answer

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 :

← Didn't Know|Knew It →

Question

A given right triangle has a hypotenuse of and a total area of . What is the height of the triangle?

Tap to reveal answer

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?

Tap to reveal answer

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?

Tap to reveal answer

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?

Tap to reveal answer

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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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?

Tap to reveal answer

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:

$4\cdot4=16$

← Didn't Know|Knew It →

Question

A given right triangle has a base of length and a total area of . What is the height of the right triangle?

Tap to reveal answer

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 :

← Didn't Know|Knew It →

Question

A given right triangle has a base length of and a total area of . What is the height of the triangle?

Tap to reveal answer

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 :

← Didn't Know|Knew It →

Question

A given right triangle has a hypotenuse of and a total area of . What is the height of the triangle?

Tap to reveal answer

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 .

← Didn't Know|Knew It →

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?

Tap to reveal answer

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?

Tap to reveal answer

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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