# what is the length of the hypotenuse of a right triangle with legs of length 7 and 8

Question
what is the length of the hypotenuse of a right triangle with legs of length 7 and 8

2021-02-10
By the Pythagorean Theorem, the sum of the squares of the leg lengths aa and bb is equal to the square of the hypotenuse cc in a right triangle:
$$\displaystyle{a}^{{2}}+{b}^{{2}}={c}^{{2}}$$
Hence, $$\displaystyle{7}^{{2}}+{8}^{{2}}={c}^{{2}}$$
$$\displaystyle{49}+{64}={c}^{{2}}$$
$$\displaystyle{113}={c}^{{2}}$$
$$\displaystyle{c}=\sqrt{{113}}\sim{10.6}$$

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