Question

The legs of an isosceles right triangle are 5 inches long. What is the length of the hypotenuse of the triangle to the nearest inch?

Answer 1

The legs are 5 inches long.

Use the Pythagorean theorem:
$5^2+5^2=c^2 \\ 25+25=c^2 \\ 50=c^2 \\ c=\sqrt{50} \\ c=\sqrt{25 \times 2} \\ c=5 \sqrt{2} \\ c \approx 7$

The length of the hypotenuse of the triangle is approximately 7 inches long.

Answer 2

$a^{2} + b^{2} = c^{2} \\ 5^{2} + 5^{2} = c^{2} \\ 25 + 25 = c^{2} \\ 50= c^{2} \\ \sqrt{50}= c \\ c=7.07$
$c$ ≈ $7$

The hypotenuse is about 7 inches long.