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If one leg of a triangle is 4 feet and the other leg is 12 feet, what is the hypotenuse?

1 Answer

Jan 2, 2016

$4 \sqrt{10} \approx 12.6491$ $4sqrt10approx12.6491$

Explanation:

The Pythagorean Theorem states that

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

where $a, b$ $a,b$ are legs in a right triangle and $c$ $c$ is the hypotenuse (the longest side).

So, we know that $a = 4$ $a=4$ and $b = 12$ $b=12$ and we want to find $c$ $c$ .

$4^{2} + 12^{2} = c^{2}$ $4^2+12^2=c^2$

$16 + 144 = c^{2}$ $16+144=c^2$

$c^{2} = 160$ $c^2=160$

$c = \sqrt{160}$ $c=sqrt160$

$c = \sqrt{16 \times 10}$ $c=sqrt(16xx10)$

$c = \sqrt{16} \times \sqrt{10}$ $c=sqrt16xxsqrt10$

$c = 4 \sqrt{10} \approx 12.6491$ $c=4sqrt10approx12.6491$

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