Question

A decent-sized square plot of land in town is one acre (1 acre = 43560 sq. Ft.). If mr Pearson wants to play football with his son Connor, then how far can they throw the football from corner to corner

Answer 1

295.16 feet

Explanation:

We need to find the length of the diagonal of a right angled triangle with equal length legs.

Length of each leg = √(43560)

Using the Pythagoras theorem:-

x^2 = (√(43560))^2 + (√(43560))^2 (where x = length of the diagonal)

x^2 = 43560 + 43560

x = √(87120) = 295.16 feet

Answer 2

distance from corner to corner = 295.16 ft

Explanation:

Given the land is square, then its area is computed as:

Area = (length of a side)^2

Replacing with area = 1 acre = 43560 sq. ft.

43560 = (length of a side)^2

length of a side = √43560

length of a side = 208.71 ft

The distance from corner to corner and two sides of the square form a right triangle, where the distance from corner to corner is the hypotenuse and the square sides are the legs. From Pythagorean theorem:

(distance from corner to corner)^2 = 208.71^2 + 208.71^2

distance from corner to corner = √(208.71^2 + 208.71^2)

distance from corner to corner = 295.16 ft