Problema Solution
The length of a rectangle is 2 more than the length of a square. The width of the rectangle is 3 less than the width of the square. The area of the rectangle is 11 less than the area of the square. What are the dimensions of the rectangle?
Answer provided by our tutors
Let the length of the square be 'a'.
Then
the length of the rectangle is: l = a + 2 (2 more than a)
the width of the rectangle is: w = a - 3 (3 less than a).
The area of the square is A1 = a*a = a^2
The area of the rectangle is A2 = w*l = (a + 2)(a - 3)
Following the conditions we have
A2 = A1 - 11 that is
(a + 2)(a - 3) = a^2 - 11
a^2 - 3a + 2a - 6 = a^2 - 11
a^2 - 11 = a^2 - 3a + 2a - 6
a^2 - 11 = a^2 - a - 6
a^2 - a^2 + a = 11 - 6
a = 5
Since
length is l = a + 2 = 5 + 2 = 7
width is w = a - 3 = 5 - 3 = 2
the dimensions of the rectangle are 7 and 2.