College algebra

Question

The combined area of a square and a rectangle is 57 square feet . The width of the rectangle is 3ft more than the length of a side of the square, and the length of the rectangle is 5 ft more than the length of a side of the square. Find the length of the rectangle. 

Answer 1

Hi Des,

 

let s = side of the square

 

w= width of rectangle

 

w = s + 3

 

l = length of rectangle

 

l = s + 5

 

area of square  = s²

 

area of rectangle = lw = (s + 3)(s + 5)

 

area of rectangle = s² + 8s + 15

 

Now add the two areas and set equal to 57

 

s² + s² + 8s + 15 = 57  get all terms on one side

 

2s² + 8s -42 = 0     divide everything by 2

 

s² + 4s - 21 = 0      factor

 

(s+7)(s - 3) = 0

 

s = -7 or s= 3  but s can't be negative

 

s = 3

 

length of the rectangle = s + 5

 

length = 8