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

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

Questions 1 - 6

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

$2\sqrt{29} in$

$4\sqrt{29}in$

Explanation

To find the length of the hypotenuse, apply the Pythagorean Theorem: , where the length of the hypotenuse.

Thus, the solution is:

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

Obtuse_isos_tri

Find the hypotenuse of the obtuse isosceles triangle shown above.

$\sqrt{180.5} ft$

$\sqrt{180}ft$

$\sqrt{90.5}ft$

Explanation

To find the length of the hypotenuse, apply the Pythagorean Theorem: , where the length of the hypotenuse.

Thus, the solution is:

$c=\sqrt{180.5}$

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

$4\sqrt{13}yds$

$16\sqrt{13}yds$

$\sqrt{144}yds$

Explanation

To find the length of the hypotenuse, apply the Pythagorean Theorem: , where the length of the hypotenuse.

Thus, the solution is:

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

Isos_obtus_tri_dos

Find the hypotenuse of the obtuse isosceles triangle shown above.

$11\sqrt{2}m$

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

$\sqrt{11}m$

$\sqrt{121}m$

Explanation

To find the length of the hypotenuse, apply the Pythagorean Theorem: , where the length of the hypotenuse.

Thus, the solution is:

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

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

$\sqrt{74} in$

$\sqrt{49}in$

Explanation

To find the length of the hypotenuse, apply the Pythagorean Theorem: , where the length of the hypotenuse.

Thus, the solution is:

$c=\sqrt{74}$

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

$20\sqrt{2}in$

$\sqrt{20}in$

Explanation

To find the length of the hypotenuse, apply the Pythagorean Theorem: , where the length of the hypotenuse.

Thus, the solution is:

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

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