application problem in linear equation

Question

The length of rectangular lot is three times its width. if the length is increased by 5 feet and the width is decreased by 2 feet, the area of lot is decreased by 21 square feet. Find the dimensions.

Answer 1

Let L = length, W = width and A = beginning area

 

L = 3W and A = LW = 3W²

 

Changed length = L + 5 = 3W + 5

Changed width = W - 2

New area = (3W + 5)(W - 2) = 3W² - W - 10

But the new area is 21 less than the initial area,  i.e. A - 21 = 3W² - 21

 

Therefore, 3W² - 21 = 3W² - W - 10

W = 11 and L = 33

 

You should check that these answers satisfy the problem.