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Intermediate Geometry : How to find the length of the hypotenuse of an acute / obtuse triangle

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Example Questions

Example Question #1 : How To Find The Length Of The Hypotenuse Of An Acute / Obtuse Triangle

An acute scalene triangle has one side length of inches and another of inches. Find the length of the hypotenuse.

Possible Answers:

$4\sqrt{29}in$

116in

$2\sqrt{29} in$

10in

Correct answer:

$2\sqrt{29} in$

Explanation:

To find the length of the hypotenuse, apply the Pythagorean Theorem: a^2+b^2=c^2 , where the length of the hypotenuse.

Thus, the solution is:

4^2+10^2=c^2

16+100=c^2

c^2=116

$c=\sqrt{116}=\sqrt{4\times 29}=\sqrt{4} \sqrt{29}=2\sqrt{29}$

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Example Question #551 : Plane Geometry

Obtuse_isos_tri

Find the hypotenuse of the obtuse isosceles triangle shown above.

Possible Answers:

$\sqrt{180}ft$

$\sqrt{90.5}ft$

$\sqrt{180.5} ft$

180ft

Correct answer:

$\sqrt{180.5} ft$

Explanation:

To find the length of the hypotenuse, apply the Pythagorean Theorem: a^2+b^2=c^2 , where the length of the hypotenuse.

Thus, the solution is:

9.5^2+9.5^2=c^2

c^2=90.25+90.25=180.5

$c=\sqrt{180.5}$

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Example Question #3 : How To Find The Length Of The Hypotenuse Of An Acute / Obtuse Triangle

A scalene triangle has one side length of yards and another side length of yards. Find the hypotenuse.

Possible Answers:

$16\sqrt{13}yds$

208yds

$4\sqrt{13}yds$

$\sqrt{144}yds$

Correct answer:

$4\sqrt{13}yds$

Explanation:

To find the length of the hypotenuse, apply the Pythagorean Theorem: a^2+b^2=c^2 , where the length of the hypotenuse.

Thus, the solution is:

12^2+8^2=c^2

c^2=144+64=208

$c=\sqrt{208}=\sqrt{16\times 13}=\sqrt{16}\sqrt{13}=4\sqrt{13}$

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Example Question #4 : How To Find The Length Of The Hypotenuse Of An Acute / Obtuse Triangle

Isos_obtus_tri_dos

Find the hypotenuse of the obtuse isosceles triangle shown above.

Possible Answers:

$\sqrt{11}\sqrt{2}m$

$\sqrt{11}m$

$11\sqrt{2}m$

$\sqrt{121}m$

Correct answer:

$11\sqrt{2}m$

Explanation:

To find the length of the hypotenuse, apply the Pythagorean Theorem: a^2+b^2=c^2 , where the length of the hypotenuse.

Thus, the solution is:

11^2+11^2=c^2

c^2=121+121=242

$c=\sqrt{242}=\sqrt{121\times 2}=\sqrt{121}\sqrt{2}=11\sqrt{2}$

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Example Question #111 : Triangles

An isosceles right triangle has two sides with a length of inches each. Find the length of the hypotenuse.

Possible Answers:

40in

$20\sqrt{2}in$

$\sqrt{20}in$

25in

Correct answer:

$20\sqrt{2}in$

Explanation:

To find the length of the hypotenuse, apply the Pythagorean Theorem: a^2+b^2=c^2 , where the length of the hypotenuse.

Thus, the solution is:

20^2+20^2=c^2

400+400=c^2

c^2=800

$c=\sqrt{800}=\sqrt{400\times 2}=\sqrt{400}\sqrt{2}=20\sqrt{2}$

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Example Question #112 : Triangles

A scalene right triangle has one side length of inches and another side length of inches. Find the length of the hypotenuse.

Possible Answers:

74in

49in

$\sqrt{74} in$

$\sqrt{49}in$

Correct answer:

$\sqrt{74} in$

Explanation:

To find the length of the hypotenuse, apply the Pythagorean Theorem: a^2+b^2=c^2 , where the length of the hypotenuse.

Thus, the solution is:

5^2+7^2=c^2

c^2=25+49=74

$c=\sqrt{74}$

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Intermediate Geometry : How to find the length of the hypotenuse of an acute / obtuse triangle

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #1 : How To Find The Length Of The Hypotenuse Of An Acute / Obtuse Triangle

Example Question #551 : Plane Geometry

Example Question #3 : How To Find The Length Of The Hypotenuse Of An Acute / Obtuse Triangle

Example Question #4 : How To Find The Length Of The Hypotenuse Of An Acute / Obtuse Triangle

Example Question #111 : Triangles

Example Question #112 : Triangles

All Intermediate Geometry Resources

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