Problema Solution
The dimensions of a rectangle are such that its length is 3
in. more than its width. If the length were doubled and if the width were decreased by 1
in., the area would be increased by 84
in.squared
.
What are the length and width of the rectangle?
Answer provided by our tutors
Let 'x' represent the original width then the length is 'x + 3'.
The area of the original rectangle is: A1 = x(x + 3)
The new doubles length is: 2(x + 3).
The new width is: x - 1
The area of the new rectangle is: A2 = (x - 1)*2(x + 3)
The new area is increased by 84 in^2:
A2 = A1 + 84
2(x - 1)(x + 3) = 84 + x(x + 3)
........
click here to see the equation solved for x
........
x = 9 in
We need to ignore the negative solution -10 since the width can not be a negative number.
The length of the rectangle is 9 + 3 = 12 in while the width is 9 in.