the length of a rectangle is 6 inches more than 4 times the width. If the area of the rectangle is 130 square inches, find the length and the width.

Question

Math help !! I'm lost

 

Answer 1

What we know:

 

Width = w

Length = 4w + 6

Area = 130 in²

 

Area = W X L = 130

So, w X (4w + 6) = 130

4w² + 6w = 130  by distributing

-130           -130

4w² + 6w - 130 = 0 

 

You can solve using the quadratic formula and by rejecting any negative lengths. 

 

Answer 2

Let w = the width

Let 4w + 6 = the length

A = lw

130 = w(4w+6)

130 = 4w² + 6w

4w² + 6w - 130 = 0    Divide both sides by 2.

2w² + 3w - 65 = 0

(2w + 13)(w - 5) = 0

2w + 13 = 0  and   w - 5 = 0

2w = -13     and    w = 5 inches

w = -6.5  (illogical answer)

l = 4w + 6  

l = 4(5) + 6 = 20 + 6

length = 26 inches