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Basic Geometry : Right Triangles

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9 Diagnostic Tests 164 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1482 : Basic Geometry

If the area of a right triangle is $\displaystyle 16$, and the base of the right triangle is $\displaystyle 4$, what is the height of the right triangle?

Possible Answers:

$\displaystyle 6$

$\displaystyle 4$

$\displaystyle 8$

$\displaystyle 2$

Correct answer:

$\displaystyle 8$

Explanation:

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$ $\displaystyle \text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Now, we are going to manipulate the equation to solve for height.

$2(\text{Area})=\text{base}\times\text{height}$ $\displaystyle 2(\text{Area})=\text{base}\times\text{height}$

$\text{Height}=\frac{2(\text{Area})}{\text{base}}$ $\displaystyle \text{Height}=\frac{2(\text{Area})}{\text{base}}$

Now, plug in the information given by the question about the values of the area and base of the triangle to find the height.

$\text{Height}=\frac{2(16)}{4}=\frac{32}{4}=8$ $\displaystyle \text{Height}=\frac{2(16)}{4}=\frac{32}{4}=8$

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Example Question #5 : How To Find The Height Of A Right Triangle

If the area of a right triangle is $\displaystyle 10$, and the base of the triangle is $\displaystyle 5$, what is the height of the triangle?

Possible Answers:

$\displaystyle 5$

$\displaystyle 2$

$\displaystyle 3$

$\displaystyle 4$

Correct answer:

$\displaystyle 4$

Explanation:

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$ $\displaystyle \text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Now, we are going to manipulate the equation to solve for height.

$2(\text{Area})=\text{base}\times\text{height}$ $\displaystyle 2(\text{Area})=\text{base}\times\text{height}$

$\text{Height}=\frac{2(\text{Area})}{\text{base}}$ $\displaystyle \text{Height}=\frac{2(\text{Area})}{\text{base}}$

Now, plug in the information given by the question about the values of the area and base of the triangle to find the height.

$\text{Height}=\frac{2(10)}{5}=\frac{20}{5}=4$ $\displaystyle \text{Height}=\frac{2(10)}{5}=\frac{20}{5}=4$

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Example Question #502 : Triangles

If the area of a right triangle is $\displaystyle 15$, and the base of the triangle is $\displaystyle 10$, what is the height of the triangle?

Possible Answers:

$\displaystyle 6$

$\displaystyle 3$

1.5 $\displaystyle 1.5$

4.5 $\displaystyle 4.5$

Correct answer:

$\displaystyle 3$

Explanation:

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$ $\displaystyle \text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Now, we are going to manipulate the equation to solve for height.

$2(\text{Area})=\text{base}\times\text{height}$ $\displaystyle 2(\text{Area})=\text{base}\times\text{height}$

$\text{Height}=\frac{2(\text{Area})}{\text{base}}$ $\displaystyle \text{Height}=\frac{2(\text{Area})}{\text{base}}$

Now, plug in the information given by the question about the values of the area and base of the triangle to find the height.

$\text{Height}=\frac{2(15)}{10}=\frac{30}{10}=3$ $\displaystyle \text{Height}=\frac{2(15)}{10}=\frac{30}{10}=3$

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Example Question #7 : How To Find The Height Of A Right Triangle

If the area of a right triangle is $\displaystyle 24$, and the base of the triangle is $\displaystyle 4$, what is the height of the triangle?

Possible Answers:

$\displaystyle 12$

$\displaystyle 8$

$\displaystyle 6$

$\displaystyle 10$

Correct answer:

$\displaystyle 12$

Explanation:

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$ $\displaystyle \text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Now, we are going to manipulate the equation to solve for height.

$2(\text{Area})=\text{base}\times\text{height}$ $\displaystyle 2(\text{Area})=\text{base}\times\text{height}$

$\text{Height}=\frac{2(\text{Area})}{\text{base}}$ $\displaystyle \text{Height}=\frac{2(\text{Area})}{\text{base}}$

Now, plug in the information given by the question about the values of the area and base of the triangle to find the height.

$\text{Height}=\frac{2(24)}{4}=\frac{48}{4}=12$ $\displaystyle \text{Height}=\frac{2(24)}{4}=\frac{48}{4}=12$

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Example Question #8 : How To Find The Height Of A Right Triangle

If the area of a right triangle is $\displaystyle 45$, and the base of the triangle is $\displaystyle 10$, what is the height of the triangle?

Possible Answers:

$\displaystyle 9$

13.5 $\displaystyle 13.5$

4.5 $\displaystyle 4.5$

$\displaystyle 18$

Correct answer:

$\displaystyle 9$

Explanation:

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$ $\displaystyle \text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Now, we are going to manipulate the equation to solve for height.

$2(\text{Area})=\text{base}\times\text{height}$ $\displaystyle 2(\text{Area})=\text{base}\times\text{height}$

$\text{Height}=\frac{2(\text{Area})}{\text{base}}$ $\displaystyle \text{Height}=\frac{2(\text{Area})}{\text{base}}$

Now, plug in the information given by the question about the values of the area and base of the triangle to find the height.

$\text{Height}=\frac{2(45)}{10}=\frac{90}{10}=9$ $\displaystyle \text{Height}=\frac{2(45)}{10}=\frac{90}{10}=9$

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Example Question #9 : How To Find The Height Of A Right Triangle

If the area of a right triangle is $\displaystyle 20$, and the base of the triangle is $\displaystyle 1$, what is the height of the triangle?

Possible Answers:

$\displaystyle 20$

$\displaystyle 40$

$\displaystyle 10$

$\displaystyle 30$

Correct answer:

$\displaystyle 40$

Explanation:

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$ $\displaystyle \text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Now, we are going to manipulate the equation to solve for height.

$2(\text{Area})=\text{base}\times\text{height}$ $\displaystyle 2(\text{Area})=\text{base}\times\text{height}$

$\text{Height}=\frac{2(\text{Area})}{\text{base}}$ $\displaystyle \text{Height}=\frac{2(\text{Area})}{\text{base}}$

Now, plug in the information given by the question about the values of the area and base of the triangle to find the height.

$\text{Height}=\frac{2(20)}{1}=\frac{40}{1}=40$ $\displaystyle \text{Height}=\frac{2(20)}{1}=\frac{40}{1}=40$

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Example Question #10 : How To Find The Height Of A Right Triangle

If the area of a right triangle is $\displaystyle 18$, and the base of the triangle is $\displaystyle 2$, what is the height of the triangle?

Possible Answers:

$\displaystyle 9$

$\displaystyle 18$

$\displaystyle 12$

$\displaystyle 20$

Correct answer:

$\displaystyle 18$

Explanation:

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$ $\displaystyle \text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Now, we are going to manipulate the equation to solve for height.

$2(\text{Area})=\text{base}\times\text{height}$ $\displaystyle 2(\text{Area})=\text{base}\times\text{height}$

$\text{Height}=\frac{2(\text{Area})}{\text{base}}$ $\displaystyle \text{Height}=\frac{2(\text{Area})}{\text{base}}$

Now, plug in the information given by the question about the values of the area and base of the triangle to find the height.

$\text{Height}=\frac{2(18)}{2}=\frac{36}{2}=18$ $\displaystyle \text{Height}=\frac{2(18)}{2}=\frac{36}{2}=18$

Report an Error

Example Question #311 : Right Triangles

If the area of a right triangle is $\displaystyle 30$, and the base of the triangle is $\displaystyle 4$, what is the height of the triangle?

Possible Answers:

$\displaystyle 10$

$\displaystyle 15$

$\displaystyle 20$

$\displaystyle 5$

Correct answer:

$\displaystyle 15$

Explanation:

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$ $\displaystyle \text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Now, we are going to manipulate the equation to solve for height.

$2(\text{Area})=\text{base}\times\text{height}$ $\displaystyle 2(\text{Area})=\text{base}\times\text{height}$

$\text{Height}=\frac{2(\text{Area})}{\text{base}}$ $\displaystyle \text{Height}=\frac{2(\text{Area})}{\text{base}}$

Now, plug in the information given by the question about the values of the area and base of the triangle to find the height.

$\text{Height}=\frac{2(30)}{4}=\frac{60}{4}=15$ $\displaystyle \text{Height}=\frac{2(30)}{4}=\frac{60}{4}=15$

Report an Error

Example Question #312 : Right Triangles

If the area of a right triangle is $\displaystyle 60$, and the base of the triangle is $\displaystyle 40$, what is the height of the triangle?

Possible Answers:

$\displaystyle 9$

$\displaystyle 12$

$\displaystyle 3$

$\displaystyle 6$

Correct answer:

$\displaystyle 3$

Explanation:

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$ $\displaystyle \text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Now, we are going to manipulate the equation to solve for height.

$2(\text{Area})=\text{base}\times\text{height}$ $\displaystyle 2(\text{Area})=\text{base}\times\text{height}$

$\text{Height}=\frac{2(\text{Area})}{\text{base}}$ $\displaystyle \text{Height}=\frac{2(\text{Area})}{\text{base}}$

Now, plug in the information given by the question about the values of the area and base of the triangle to find the height.

$\text{Height}=\frac{2(60)}{40}=\frac{120}{40}=3$ $\displaystyle \text{Height}=\frac{2(60)}{40}=\frac{120}{40}=3$

Report an Error

Example Question #313 : Right Triangles

If the area of a right triangle is $\displaystyle 22$, and the base of the triangle is $\displaystyle 11$, what is the height of the triangle?

Possible Answers:

$\displaystyle 3$

$\displaystyle 5$

$\displaystyle 2$

$\displaystyle 4$

Correct answer:

$\displaystyle 4$

Explanation:

Recall how to find the area of a right triangle:

$\text{Area}=\frac{1}{2}(\text{base}\times\text{height})$ $\displaystyle \text{Area}=\frac{1}{2}(\text{base}\times\text{height})$

Now, we are going to manipulate the equation to solve for height.

$2(\text{Area})=\text{base}\times\text{height}$ $\displaystyle 2(\text{Area})=\text{base}\times\text{height}$

$\text{Height}=\frac{2(\text{Area})}{\text{base}}$ $\displaystyle \text{Height}=\frac{2(\text{Area})}{\text{base}}$

Now, plug in the information given by the question about the values of the area and base of the triangle to find the height.

$\text{Height}=\frac{2(22)}{11}=\frac{44}{11}=4$ $\displaystyle \text{Height}=\frac{2(22)}{11}=\frac{44}{11}=4$

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Basic Geometry : Right Triangles

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #1482 : Basic Geometry

Example Question #5 : How To Find The Height Of A Right Triangle

Example Question #502 : Triangles

Example Question #7 : How To Find The Height Of A Right Triangle

Example Question #8 : How To Find The Height Of A Right Triangle

Example Question #9 : How To Find The Height Of A Right Triangle

Example Question #10 : How To Find The Height Of A Right Triangle

Example Question #311 : Right Triangles

Example Question #312 : Right Triangles

Example Question #313 : Right Triangles

All Basic Geometry Resources

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