what distance produces a picture with an area of 100 sq ft?

Question

The area of a projected picture on a movie screen varies directly as the square of the distance from the projector to the screen. If a distance of 40 feet produces a picture with an area of 64 square feet, what distance (in ft) produces a picture with an area of 100 square feet?

Answer 1

64 = k40^2 = 1600k

k = 64/1600 = 4/100 = .04 = 1/25

A = d^2/25

100 = d^2/25

d^2 = 2500

d = 50 feet