Question

what is the measure of the hypotenuse to the nearest tenth of a metre? a) 45.3 m b) 64.0 m c) 90.5 m d) 35.8 m

Explanation:

Step1: Find side - length of square

The area of the square is $A = 256m^{2}$. Using the formula $A = s^{2}$ (where $s$ is the side - length of the square), we solve for $s$: $s=\sqrt{256}=16m$.

Step2: Identify right - triangle sides

In the right - triangle, one leg $a = 16m$ and the other leg $b = 32m$.

Step3: Apply Pythagorean theorem

The Pythagorean theorem is $c^{2}=a^{2}+b^{2}$, where $c$ is the hypotenuse. Substitute $a = 16$ and $b = 32$ into the formula: $c^{2}=16^{2}+32^{2}=256 + 1024=1280$.

Step4: Calculate the hypotenuse

$c=\sqrt{1280}\approx35.8m$.

Answer:

d) $35.8m$