Question

a football field has the shape of a rectangle with dimensions of 300 feet long and 160 feet wide. if a fan was to run diagonally from one end zone to the opposite end zone, how far would she run to the nearest foot? enter only the number. 300 feet 160 feet the solution is

Explanation:

Step1: Apply the Pythagorean theorem

The Pythagorean theorem for a right - triangle is \(a^{2}+b^{2}=c^{2}\), where \(a = 160\), \(b = 300\), and \(c\) is the length of the diagonal.
So, \(c=\sqrt{160^{2}+300^{2}}\).

Step2: Calculate \(160^{2}\) and \(300^{2}\)

\(160^{2}=160\times160 = 25600\), \(300^{2}=300\times300=90000\).
Then \(160^{2}+300^{2}=25600 + 90000=115600\).

Step3: Find the square root

\(c=\sqrt{115600}\). Since \(340^{2}=115600\) (because \(340\times340=(300 + 40)\times(300 + 40)=300^{2}+2\times300\times40+40^{2}=90000+24000 + 1600=115600\)).

Answer:

340