The length of a rectangle is three more than twice the width. The area of the rectangle is 27 meters squared. Find the dimensions and area of the rectangle

Question

The length of a rectangle is three more than twice the width. The area of the rectangle is 27 meters squared. Find the dimensions and area of the rectangle

Answer 1

We know that the Area of a rectangle = Length x Width

 

Let w = width; then l = 2w + 3; we are given that a = 27m²

 

then 27m² = w(2w + 3)

 

27m² = 2w² + 3w, which can be written as 2w² + 3w - 27m² = 0

the factors of 27 are 27 and 1, and 9 and 3

we can factor the expression as follows: (2w + 9)(w - 3) = 0

 

we see that 2w + 9 = 0  yields a negative length, so it must be discarded

 

then w - 3 = 0 becomes w = 3

substituting this value, we get 2w + 3 = 9

so, the dimensions are 9m and 3m, which when multiplied together yield 27m²