Question

a rectangle is 28 feet by 41 feet. If it can be determined, which of the following gives the whole number length, in feet, of a side of the largest square that will fit inside the rectangle?

Answer 1

c = 20 ft

Explanation:

The largest square will be 14 sqrt(2) ft long

To figure out the side length of the square

use the pythagorean theorem

a^2 + b^2 =c^2

we are limited by the shortest side of the rectangle

28 ft

each side of the triangle is 1/2 the length of the short side of the rectangle or 14 ft

a^2 + b^2 =c^2

14^2 + 14^2 = c^2 where c is the side of the square

196 + 196 = c^2

392 = c^2

take the square root of each side

sqrt(392) = sqrt(c^2)

c = 14sqrt(2)

c = 19.799ft

to the nearest whole number

c = 20 ft