Question

A football field is 100 yards with 10 yards at each end for the end zones. The field is 45 yards wide. Find the length of the diagonal of the entire field, including endzones

Answer 1

The formula for the diagonal of a rectangle is:

$\sf d=\sqrt{l^2+w^2}$

The length would be the 100 yards plus the two endzones. 100 + 10 + 10 = 120. The width is 45 yards. Plug these into the formula:

$\sf d=\sqrt{120^2+45^2}$

Simplify the exponents:

$\sf d=\sqrt{14400+2025}$

Add:

$\sf d=\sqrt{16425}\rightarrow\boxed{\sf 15\sqrt{73}~yds}$

Or if you want an approximate answer:

$\sf 15\sqrt{73}\approx 128.16~yds$

Answer 2

you could use pythagorean theorem: a^2+b^2=c^2

100^2+45^2=c^2

10,000+2,025=12,025

square root of 12,025 is 109.6

109.6 is your answer