Question

What is the length of the hypotenuse?If necessary,round to the nearest tenth

Answer 1

Answer:

85 yd

Step-by-step explanation:

We know that

$\pmb{\bf H^2=P^2+B^2}$

Here,

H = c, P = 75 yd, B = 40 yd

$\begin{gathered} \: \sf \implies \: {c }^{2} = (75) {}^{2} + {(40)}^{2} \\ \sf \implies {c}^{2} = 5625 + 1600 \\ \sf \implies \: {c}^{2} = 7225 \\ \sf \implies \: c = \sqrt{7225} \\ \sf \implies \: c = 85 \: yd \end{gathered}$

Answer 2

Answer:  85

Work Shown:

$a^2 + b^2 = c^2\\\\40^2 + 75^2 = c^2\\\\1600 + 5625 = c^2\\\\7225 = c^2\\\\c^2 = 7225\\\\c = \sqrt{7225}\\\\c = 85$

I used the pythagorean theorem with a = 40 and b = 75. The order of the 'a' and b doesn't matter, as long as c is the largest side.

The 40-75-85 pythagorean triple is the scaled up version of the 8-15-17 triple (multiply each piece by 5).