Question

a standard city block is a square with each side measuring 117 yards. find the length of the diagonal of a city block. the length of the diagonal is approximately (round to the nearest hundredth as needed.) sq. yd. yd. cu. yd.

Explanation:

Step1: Recall Pythagorean theorem for square

For a square with side length \( s \), the diagonal \( d \) satisfies \( d^{2}=s^{2}+s^{2}=2s^{2} \), so \( d = s\sqrt{2} \).
Here, \( s = 117 \) yards.

Step2: Calculate the diagonal length

Substitute \( s = 117 \) into the formula: \( d=117\times\sqrt{2} \).
\( \sqrt{2}\approx1.4142 \), so \( d = 117\times1.4142\approx165.46 \) yards.

Answer:

165.46 yd.