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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 $\displaystyle 4$ inches and another of $\displaystyle 10$ inches. Find the length of the hypotenuse.

Possible Answers:

$2\sqrt{29} in$ $\displaystyle 2\sqrt{29} in$

116in $\displaystyle 116in$

10in $\displaystyle 10in$

$4\sqrt{29}in$ $\displaystyle 4\sqrt{29}in$

Correct answer:

$2\sqrt{29} in$ $\displaystyle 2\sqrt{29} in$

Explanation:

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

Thus, the solution is:

$\displaystyle 4^2+10^2=c^2$

$\displaystyle 16+100=c^2$

c^2=116 $\displaystyle c^2=116$

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

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Example Question #552 : Intermediate Geometry

Obtuse_isos_tri

Find the hypotenuse of the obtuse isosceles triangle shown above.

Possible Answers:

$\sqrt{180}ft$ $\displaystyle \sqrt{180}ft$

180ft $\displaystyle 180ft$

$\sqrt{90.5}ft$ $\displaystyle \sqrt{90.5}ft$

$\sqrt{180.5} ft$ $\displaystyle \sqrt{180.5} ft$

Correct answer:

$\sqrt{180.5} ft$ $\displaystyle \sqrt{180.5} ft$

Explanation:

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

Thus, the solution is:

$\displaystyle 9.5^2+9.5^2=c^2$

$\displaystyle c^2=90.25+90.25=180.5$

$c=\sqrt{180.5}$ $\displaystyle c=\sqrt{180.5}$

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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 $\displaystyle 12$ yards and another side length of $\displaystyle 8$ yards. Find the hypotenuse.

Possible Answers:

$16\sqrt{13}yds$ $\displaystyle 16\sqrt{13}yds$

208yds $\displaystyle 208yds$

$4\sqrt{13}yds$ $\displaystyle 4\sqrt{13}yds$

$\sqrt{144}yds$ $\displaystyle \sqrt{144}yds$

Correct answer:

$4\sqrt{13}yds$ $\displaystyle 4\sqrt{13}yds$

Explanation:

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

Thus, the solution is:

$\displaystyle 12^2+8^2=c^2$

$\displaystyle c^2=144+64=208$

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

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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:

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

$\sqrt{11}m$ $\displaystyle \sqrt{11}m$

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

$\sqrt{121}m$ $\displaystyle \sqrt{121}m$

Correct answer:

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

Explanation:

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

Thus, the solution is:

$\displaystyle 11^2+11^2=c^2$

$\displaystyle c^2=121+121=242$

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

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

An isosceles right triangle has two sides with a length of $\displaystyle 20$ inches each. Find the length of the hypotenuse.

Possible Answers:

40in $\displaystyle 40in$

$\sqrt{20}in$ $\displaystyle \sqrt{20}in$

25in $\displaystyle 25in$

$20\sqrt{2}in$ $\displaystyle 20\sqrt{2}in$

Correct answer:

$20\sqrt{2}in$ $\displaystyle 20\sqrt{2}in$

Explanation:

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

Thus, the solution is:

$\displaystyle 20^2+20^2=c^2$

$\displaystyle 400+400=c^2$

c^2=800 $\displaystyle c^2=800$

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

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Example Question #112 : Triangles

A scalene right triangle has one side length of $\displaystyle 5$ inches and another side length of $\displaystyle 7$ inches. Find the length of the hypotenuse.

Possible Answers:

74in $\displaystyle 74in$

49in $\displaystyle 49in$

$\sqrt{74} in$ $\displaystyle \sqrt{74} in$

$\sqrt{49}in$ $\displaystyle \sqrt{49}in$

Correct answer:

$\sqrt{74} in$ $\displaystyle \sqrt{74} in$

Explanation:

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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 #552 : Intermediate 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 #1 : How To Find The Length Of The Hypotenuse Of An Acute / Obtuse Triangle

Example Question #112 : Triangles

All Intermediate Geometry Resources

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