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Basic Geometry : Right Triangles

Study concepts, example questions & explanations for Basic Geometry

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

Example Questions

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Example Question #81 : Triangles

Square PQRS is on the coordinate plane, and each side of the square is parallel to either the -axis or -axis. Point has coordinates $\left ( -2,-1 \right )$ and point has the coordinates $\left ( 3,4 \right )$ .

Quantity A: $5\sqrt{2}$

Quantity B: The distance between points and

Possible Answers:

Quantity A is greater.

The two quantities are equal.

Quantity B is greater.

The relationship cannot be determined from the information provided.

Correct answer:

The two quantities are equal.

Explanation:

To find the distance between points and , split the square into two 45-45-90 triangles and find the hypotenuse. The side ratio of the 45-45-90 triangle is $s:s:s\sqrt{2}$ , so if the sides have a length of 5, the hypotenuse must be $5\sqrt{2}$ .

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Example Question #51 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Given the two perpendicular sides of a triangle are and , find the hypotenuse.

Possible Answers:

$\sqrt{58}$

$\sqrt{21}$

Correct answer:

$\sqrt{58}$

Explanation:

To find the length of the hypotenuse, you must use the pythagorean theorem.

c^2=a^2+b^2=3^2+7^2=9+49=58

$c^2=58\Rightarrow c=\sqrt{58}$

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Example Question #51 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Find the length of the hypotenuse of the following right triangle.

Possible Answers:

Correct answer:

Explanation:

Recall the Pythagorean Theorem, which is used to find the length of the hypotenuse.

For any triangle with leg lengths of and ,

$\text{Hypotenuse}^2=a^2+b^2$

Take the square root of both sides to find the length of the hypotenuse.

$\text{Hypotenuse}=\sqrt{a^2+b^2}$

Plug in the given values to find the length of the hypotenuse.

$\text{Hypotenuse}=\sqrt{12^2 + 16^2}=\sqrt{400}=20$

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Example Question #112 : Geometry

Find the length of the hypotenuse of the following right triangle.

Possible Answers:

256

$2\sqrt{113}$

$6\sqrt{13}$

$2\sqrt{111}$

Correct answer:

$2\sqrt{113}$

Explanation:

Recall the Pythagorean Theorem, which is used to find the length of the hypotenuse.

For any triangle with leg lengths of and ,

$\text{Hypotenuse}^2=a^2+b^2$

Take the square root of both sides to find the length of the hypotenuse.

$\text{Hypotenuse}=\sqrt{a^2+b^2}$

Plug in the given values to find the length of the hypotenuse.

$\text{Hypotenuse}=\sqrt{14^2 + 16^2}=\sqrt{452}=2\sqrt{113}$

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Example Question #113 : Geometry

Find the length of the hypotenuse of the following right triangle.

Possible Answers:

$4\sqrt5$

$2\sqrt5$

$3\sqrt5$

$\sqrt5$

Correct answer:

$2\sqrt5$

Explanation:

Recall the Pythagorean Theorem, which is used to find the length of the hypotenuse.

For any triangle with leg lengths of and ,

$\text{Hypotenuse}^2=a^2+b^2$

Take the square root of both sides to find the length of the hypotenuse.

$\text{Hypotenuse}=\sqrt{a^2+b^2}$

Plug in the given values to find the length of the hypotenuse.

$\text{Hypotenuse}=\sqrt{2^2 + 4^2}=\sqrt{20}=2\sqrt5$

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Example Question #114 : Geometry

Find the length of the hypotenuse of the following right triangle.

Possible Answers:

$2\sqrt{10}$

$5\sqrt5$

$4\sqrt5$

$6\sqrt5$

Correct answer:

$5\sqrt5$

Explanation:

Recall the Pythagorean Theorem, which is used to find the length of the hypotenuse.

For any triangle with leg lengths of and ,

$\text{Hypotenuse}^2=a^2+b^2$

Take the square root of both sides to find the length of the hypotenuse.

$\text{Hypotenuse}=\sqrt{a^2+b^2}$

Plug in the given values to find the length of the hypotenuse.

$\text{Hypotenuse}=\sqrt{5^2 + 10^2}=\sqrt{125}=5\sqrt5$

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Example Question #51 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Find the length of the hypotenuse of the following right triangle.

Possible Answers:

$\sqrt{26}$

$3\sqrt3$

$2\sqrt6$

Correct answer:

$\sqrt{26}$

Explanation:

Recall the Pythagorean Theorem, which is used to find the length of the hypotenuse.

For any triangle with leg lengths of and ,

$\text{Hypotenuse}^2=a^2+b^2$

Take the square root of both sides to find the length of the hypotenuse.

$\text{Hypotenuse}=\sqrt{a^2+b^2}$

Plug in the given values to find the length of the hypotenuse.

$\text{Hypotenuse}=\sqrt{1^2 + 5^2}=\sqrt{26}$

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Example Question #16 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

Find the length of the hypotenuse of the following right triangle.

Possible Answers:

$4\sqrt{41}$

$2\sqrt{41}$

$3\sqrt{41}$

$\sqrt{41}$

Correct answer:

$3\sqrt{41}$

Explanation:

Recall the Pythagorean Theorem, which is used to find the length of the hypotenuse.

For any triangle with leg lengths of and ,

$\text{Hypotenuse}^2=a^2+b^2$

Take the square root of both sides to find the length of the hypotenuse.

$\text{Hypotenuse}=\sqrt{a^2+b^2}$

Plug in the given values to find the length of the hypotenuse.

$\text{Hypotenuse}=\sqrt{15^2 + 12^2}=\sqrt{369}=3\sqrt{41}$

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Example Question #115 : Geometry

Find the length of the hypotenuse of the following right triangle.

Possible Answers:

Correct answer:

Explanation:

Recall the Pythagorean Theorem, which is used to find the length of the hypotenuse.

For any triangle with leg lengths of and ,

$\text{Hypotenuse}^2=a^2+b^2$

Take the square root of both sides to find the length of the hypotenuse.

$\text{Hypotenuse}=\sqrt{a^2+b^2}$

Plug in the given values to find the length of the hypotenuse.

$\text{Hypotenuse}=\sqrt{12^2 + 5^2}=\sqrt{169}=13$

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Example Question #116 : Geometry

Find the length of the hypotenuse of the following right triangle.

Possible Answers:

$15\sqrt{2}$

$\sqrt{346}$

$\sqrt{347}$

$10\sqrt3$

Correct answer:

$\sqrt{346}$

Explanation:

Recall the Pythagorean Theorem, which is used to find the length of the hypotenuse.

For any triangle with leg lengths of and ,

$\text{Hypotenuse}^2=a^2+b^2$

Take the square root of both sides to find the length of the hypotenuse.

$\text{Hypotenuse}=\sqrt{a^2+b^2}$

Plug in the given values to find the length of the hypotenuse.

$\text{Hypotenuse}=\sqrt{15^2 + 11^2}=\sqrt{346}$

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Basic Geometry : Right Triangles

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #81 : Triangles

Example Question #51 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #51 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #112 : Geometry

Example Question #113 : Geometry

Example Question #114 : Geometry

Example Question #51 : How To Find The Length Of The Hypotenuse Of A Right Triangle : Pythagorean Theorem

Example Question #16 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

Example Question #115 : Geometry

Example Question #116 : Geometry

All Basic Geometry Resources

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