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Basic Geometry : How to find the length of the hypotenuse of a 45/45/90 right isosceles triangle : Pythagorean Theorem

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Example Questions

Example Question #991 : Basic Geometry

Find the length of the hypotenuse.

Possible Answers:

$6\sqrt2$

$2\sqrt3$

$6\sqrt3$

Correct answer:

$6\sqrt2$

Explanation:

To find the hypotenuse of a triangle, you can use the Pythagorean Theorem. For any right triangle with leg lengths of and and a hypotenuse of ,

c^2=a^2+b^2

$c=\sqrt{a^2+b^2}$

Now, plug in the values of and from the question.

$\text{Hypotenuse}=\sqrt{6^2+6^2}$

$\text{Hypotenuse}=\sqrt{36+36}$

Solve.

$\text{Hypotenuse}=\sqrt{72}$

Simplify.

$\text{Hypotenuse}=6\sqrt2$

Report an Error

Example Question #992 : Plane Geometry

Find the length of the hypotenuse.

Possible Answers:

$2\sqrt6$

$4\sqrt6$

$12\sqrt3$

$12\sqrt2$

Correct answer:

$12\sqrt2$

Explanation:

To find the hypotenuse of a triangle, you can use the Pythagorean Theorem. For any right triangle with leg lengths of and and a hypotenuse of ,

c^2=a^2+b^2

$c=\sqrt{a^2+b^2}$

Now, plug in the values of and from the question.

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

$\text{Hypotenuse}=\sqrt{144+144}$

Solve.

$\text{Hypotenuse}{}=\sqrt{288}$

Simplify.

$\text{Hypotenuse}=12\sqrt2$

Report an Error

Example Question #991 : Basic Geometry

Find the length of the hypotenuse.

Possible Answers:

$13\sqrt3$

$13\sqrt2$

$\sqrt{26}$

Correct answer:

$13\sqrt2$

Explanation:

To find the hypotenuse of a triangle, you can use the Pythagorean Theorem. For any right triangle with leg lengths of and and a hypotenuse of ,

c^2=a^2+b^2

$c=\sqrt{a^2+b^2}$

Now, plug in the values of and from the question.

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

$\text{Hypotenuse}=\sqrt{169+169}$

Solve.

$\text{Hypotenuse}=\sqrt{338}$

Simplify.

$\text{Hypotenuse}=13\sqrt2$

Report an Error

Example Question #994 : Plane Geometry

Find the length of the hypotenuse.

Possible Answers:

$14\sqrt2$

$14\sqrt3$

$7\sqrt7$

$2\sqrt7$

Correct answer:

$14\sqrt2$

Explanation:

To find the hypotenuse of a triangle, you can use the Pythagorean Theorem. For any right triangle with leg lengths of and and a hypotenuse of ,

c^2=a^2+b^2

$c=\sqrt{a^2+b^2}$

Now, plug in the values of and from the question.

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

$\text{Hypotenuse}=\sqrt{196+196}$

Solve.

$\text{Hypotenuse}=\sqrt{392}$

Simplify.

$\text{Hypotenuse}=14\sqrt2$

Report an Error

Example Question #995 : Plane Geometry

Find the length of the hypotenuse.

Possible Answers:

$4\sqrt{10}$

$24\sqrt2$

$14\sqrt6$

$4\sqrt3$

Correct answer:

$24\sqrt2$

Explanation:

To find the hypotenuse of a triangle, you can use the Pythagorean Theorem. For any right triangle with leg lengths of and and a hypotenuse of ,

c^2=a^2+b^2

$c=\sqrt{a^2+b^2}$

Now, plug in the values of and from the question.

$\text{Hypotenuse}=\sqrt{24^2+24^2}$

$\text{Hypotenuse}=\sqrt{576+576}$

Solve.

$\text{Hypotenuse}=\sqrt{1152}$

Simplify.

$\text{Hypotenuse}=24\sqrt2$

Report an Error

Example Question #996 : Plane Geometry

Find the length of the hypotenuse.

Possible Answers:

$15\sqrt2$

$4\sqrt{10}$

$22\sqrt2$

$2\sqrt{11}$

Correct answer:

$22\sqrt2$

Explanation:

To find the hypotenuse of a triangle, you can use the Pythagorean Theorem. For any right triangle with leg lengths of and and a hypotenuse of ,

c^2=a^2+b^2

$c=\sqrt{a^2+b^2}$

Now, plug in the values of and from the question.

$\text{Hypotenuse}=\sqrt{22^2+22^2}$

$\text{Hypotenuse}=\sqrt{484+484}$

Solve.

$\text{Hypotenuse}=\sqrt{968}$

Simplify.

$\text{Hypotenuse}=22\sqrt2$

Report an Error

Example Question #997 : Plane Geometry

Find the length of the hypotenuse.

Possible Answers:

$25\sqrt2$

$5\sqrt2$

Correct answer:

$25\sqrt2$

Explanation:

To find the hypotenuse of a triangle, you can use the Pythagorean Theorem. For any right triangle with leg lengths of and and a hypotenuse of ,

c^2=a^2+b^2

$c=\sqrt{a^2+b^2}$

Now, plug in the values of and from the question.

$\text{Hypotenuse}=\sqrt{25^2+25^2}$

$\text{Hypotenuse}=\sqrt{625+625}$

Solve.

$\text{Hypotenuse}=\sqrt{1250}$

Simplify.

$\text{Hypotenuse}=25\sqrt2$

Report an Error

Example Question #11 : Triangles

Find the length of the hypotenuse.

Possible Answers:

145

$145\sqrt3$

290

$145\sqrt2$

Correct answer:

$145\sqrt2$

Explanation:

To find the hypotenuse of a triangle, you can use the Pythagorean Theorem. For any right triangle with leg lengths of and and a hypotenuse of ,

c^2=a^2+b^2

$c=\sqrt{a^2+b^2}$

Now, plug in the values of and from the question.

$\text{Hypotenuse}=\sqrt{145^2+145^2}$

$\text{Hypotenuse}=\sqrt{21025+21025}$

Solve.

$\text{Hypotenuse}=\sqrt{42050}$

Simplify.

$\text{Hypotenuse}=145\sqrt2$

Report an Error

Example Question #12 : Triangles

Find the length of the hypotenuse.

Possible Answers:

$19\sqrt3$

$19\sqrt2$

$28\sqrt2$

Correct answer:

$19\sqrt2$

Explanation:

To find the hypotenuse of a triangle, you can use the Pythagorean Theorem. For any right triangle with leg lengths of and and a hypotenuse of ,

c^2=a^2+b^2

$c=\sqrt{a^2+b^2}$

Now, plug in the values of and from the question.

$\text{Hypotenuse}=\sqrt{19^2+19^2}$

$\text{Hypotenuse}=\sqrt{361+361}$

Solve.

$\text{Hypotenuse}=\sqrt{722}$

Simplify.

$\text{Hypotenuse}=19\sqrt2$

Report an Error

Example Question #13 : Triangles

Find the length of the hypotenuse.

Possible Answers:

$21\sqrt2$

$21\sqrt3$

$\sqrt{42}$

$10\sqrt5$

Correct answer:

$21\sqrt2$

Explanation:

To find the hypotenuse of a triangle, you can use the Pythagorean Theorem. For any right triangle with leg lengths of and and a hypotenuse of ,

c^2=a^2+b^2

$c=\sqrt{a^2+b^2}$

Now, plug in the values of and from the question.

$\text{Hypotenuse}=\sqrt{21^2+21^2}$

$\text{Hypotenuse}=\sqrt{441^2+441}$

Solve.

$\text{Hypotenuse}=\sqrt{882}$

Simplify.

$\text{Hypotenuse}=21\sqrt2$

Report an Error

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Basic Geometry : How to find the length of the hypotenuse of a 45/45/90 right isosceles triangle : Pythagorean Theorem

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #991 : Basic Geometry

Example Question #992 : Plane Geometry

Example Question #991 : Basic Geometry

Example Question #994 : Plane Geometry

Example Question #995 : Plane Geometry

Example Question #996 : Plane Geometry

Example Question #997 : Plane Geometry

Example Question #11 : Triangles

Example Question #12 : Triangles

Example Question #13 : Triangles

All Basic Geometry Resources

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