Question

A corner lot had dimensions 20 x 40 metered before it lost two strips of equal width when the adjacent streets were widened. Find the new dimensions of the lot if it's area is now 525 square meters.

Answer 1

15 m by 35 m

Explanation:

If x represents the width of the strip lost (in meters), then the new area is ...

(20-x)(40-x) = 525

800 -60x +x^2 = 525

x^2 -60x +900 = 625 . . . . add 100 to complete the square

(x -30)^2 = 25^2

x = 30 ±25

The width must be less than 20, so the solution x=55 is extraneous. The lost width is 5 meters, so the new lot dimensions are 20-5 = 15 by 40-5 = 35.

The lot is now 15 m by 35 m.

_____

It is obvious that 25 is a factor of the new area, suggesting that 5 is the width of interest. "Guess and check" works well in this case.