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Basic Geometry : Triangles

Study concepts, example questions & explanations for Basic Geometry

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All Basic Geometry Resources

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

Example Questions

Example Question #425 : Grade 8

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

Possible Answers:

$3\sqrt3$

$\sqrt{26}$

$2\sqrt6$

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.

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

Report an Error

Example Question #431 : Grade 8

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

Possible Answers:

$2\sqrt{41}$

$3\sqrt{41}$

$\sqrt{41}$

$4\sqrt{41}$

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.

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

Report an Error

Example Question #291 : Triangles

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.

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

Report an Error

Example Question #291 : Triangles

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

Possible Answers:

$\sqrt{346}$

$15\sqrt{2}$

$\sqrt{347}$

$10\sqrt3$

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.

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

Report an Error

Example Question #23 : 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:

$\sqrt{271}$

$\sqrt{269}$

$3\sqrt{30}$

$2\sqrt{67}$

Correct answer:

$\sqrt{269}$

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.

$\text{Hypotenuse}=\sqrt{10^2 + 13^2}=\sqrt{269}$

Report an Error

Example Question #24 : 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:

$\sqrt{34}$

$\sqrt{33}$

$\sqrt{35}$

Correct answer:

$\sqrt{34}$

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.

$\text{Hypotenuse}=\sqrt{3^2 + 5^2}=\sqrt{34}$

Report an Error

Example Question #292 : Triangles

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

Possible Answers:

$\sqrt{66}$

$\sqrt{65}$

$\sqrt{69}$

Correct answer:

$\sqrt{65}$

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.

$\text{Hypotenuse}=\sqrt{7^2 + 4^2}=\sqrt{65}$

Report an Error

Example Question #1281 : Basic Geometry

Find the length of the hypotenuse.

Possible Answers:

$3\sqrt3$

$\sqrt{15}$

$\sqrt{14}$

$4\sqrt2$

Correct answer:

$\sqrt{14}$

Explanation:

Recall how to find the length of the hypotenuse, , of a right triangle by using the Pythagorean Theorem.

a^2+b^2=c^2

Substitute in the given values.

$c^2=(\sqrt6)^2+(2\sqrt2)^2$

Simplify.

c^2=6+8

Solve.

c^2=14

Now, because we want to solve for just , take the square root of the value you found above.

$\sqrt{c^2}=c=\sqrt{14}$

Report an Error

Example Question #292 : Triangles

Find the length of the hypotenuse.

Possible Answers:

$4\sqrt5$

$6\sqrt2$

$\sqrt{26}$

Correct answer:

Explanation:

Recall how to find the length of the hypotenuse, , of a right triangle by using the Pythagorean Theorem.

a^2+b^2=c^2

Substitute in the given values.

$c^2=(\sqrt6)^2+(\sqrt{19})^2$

Simplify.

c^2=6+19

Solve.

c^2=25

Now, because we want to solve for just , take the square root of the value you found above.

$\sqrt{c^2}=\sqrt{25}$

Simplify.

c=5

Report an Error

Example Question #293 : Triangles

Find the length of the hypotenuse.

Possible Answers:

$2\sqrt3$

$2\sqrt6$

$5\sqrt2$

Correct answer:

Explanation:

Recall how to find the length of the hypotenuse, , of a right triangle by using the Pythagorean Theorem.

a^2+b^2=c^2

Substitute in the given values.

$c^2=(\sqrt{11})^2+(\sqrt{14})^2$

Simplify.

c^2=11+14

Solve.

c^2=25

Now, because we want to solve for just , take the square root of the value you found above.

$\sqrt{c^2}=\sqrt{25}$

Simplify.

c=5

Report an Error

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All Basic Geometry Resources

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Basic Geometry : Triangles

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #425 : Grade 8

Example Question #431 : Grade 8

Example Question #291 : Triangles

Example Question #291 : Triangles

Example Question #23 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

Example Question #24 : Apply The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles: Ccss.Math.Content.8.G.B.7

Example Question #292 : Triangles

Example Question #1281 : Basic Geometry

Example Question #292 : Triangles

Example Question #293 : Triangles

All Basic Geometry Resources

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