Question

unit 3 - geometry
question 46, 6.6.51
hw score: 94.83%, 55 of 58 points
points: 0 of 1
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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.)

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: Substitute and calculate

Substitute \( s = 117 \) into the formula: \( d=117\times\sqrt{2} \).
Calculate \( \sqrt{2}\approx1.4142 \), then \( d = 117\times1.4142\approx165.46 \) (rounded to nearest hundredth).

Answer:

165.46