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' represent the decreased amount, x>0,
the dimensions of the new rectangle are: 20 - x and 23 - x
also the new dimensions must be positive thus
20 - x > 0
x < 20
23 - x > 0
x < 23
the area of the original rectangle is: 20*23
the area of the new rectangle is: (20 - x)(23 - x)
the area of the rectangle decreased by 120 cm^2 means:
(20 - x)(23 - x) = 20*23 - 120
by solving we find:
x = 3 cm
click here to see the step by step solution of the quadrativ equation:
20 - 3 = 17 cm
23 - 3 = 20 cm
the dimensions of the new rectangle are 17 cm and 20 cm.