The area of a rectangle is 63ft^2, and the length of a rectangle is 5 foot more than twice the width. Find the dimensions of the rectangle.

Question

The area of a rectangle is 63ft^2, and the length of a rectangle is 5 foot more than twice the width. Find the dimensions of the rectangle.

Answer 1

Area of rectangle = length X width 

 

length = 5 + 2w

width  = w 

 

Area of rectangle = 63 = (5+2w) (w) = 5w + 2w² 

 

Rearrange for the following:

 

2w² +5w - 63 = 0 

 

Now, factor. Remember you will multiply the a term (2) and the c term (-63). Then you will find multiples of -126 (2*-63) that add up to 5 (b term):

 

(2w + 14) (2w - 9) 

 

Reduce for the following:

 

(w+7)(2w-9)

 

Check by expanding the expression: 2w² - 9w +14w - 63 

 

Now solve for the following:

 

w = - 7

w = 4.5 

 

Since we cannot have a negative width, our answer is 4.5. Let's check: 

 

Area of rectangle = 63 = (5+2w) (w) = 5w + 2w² = 5(4.5) + 2(4.5)² = 63 

 

Hope that helps!