Question

what is the measure of the hypotenuse? a) 13 m b) 20.5 m c) 29 m d) 20 m

Explanation:

Step1: Find side - length of square

The area of the square is $A = s^{2}=441\ m^{2}$, so $s=\sqrt{441}=21\ m$.

Step2: Identify right - triangle sides

In the right - triangle below the square, one leg is $20\ m$ and the other is $21\ m$.

Step3: Apply Pythagorean theorem

The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$, where $a = 20\ m$ and $b = 21\ m$. Then $c=\sqrt{20^{2}+21^{2}}=\sqrt{400 + 441}=\sqrt{841}=29\ m$.

Answer:

c) $29\ m$