Problema Solution
Originally the dimensions of a rectangle were 20 cm by 23 cm. When both dimensions were decreased by the same amount, the area of the rectangle decreased by 120 cm^2. find the dimensions of the new rectangle.
Answer provided by our tutors
let
x = the amount of decreasing, x>0, x<=20
l = 23 cm the length of the rectangle
w = 20 cm the width of the rectangle
l - x = 23 - x the decreased length
w - x = 20 - x the decreased width
the area of the original rectangle is A1 = l*w
the area of the decreased rectangle is A2 = (l - x)(w - x)
A1 - A2 = 120
l*w - (l - x)(w - x) = 120
23*20 - (23 - x)(20 - x) = 120
by solving we find:
x = 3 cm
click here to see the step by step solution of the equation:
23 - 3 = 20 cm
20 - 3 = 17 cm
the dimensions of the new rectangle are: the length is 20 cm and the width is 17 cm.