Finding length and width when only given area

Question

A rectangle had an area of 112 square inches and a width which is 5 inches less than 3 times the length, find the length and width of the rectangle 

 

Answer 1

Hi Kylee,

 

Let the length be x inches. Then, the width, w, can be expressed as

w = (3x - 5) in

 

Area, A = w*l

112 = x(3x - 5)

112 = 3x^2 - 5x

3x^2 - 5x - 112 = 0

(3x + 16)(x - 7) = 0

3x + 16 = 0 (not valid)

x - 7 = 0

x = 7 in (this is the length)

w = 3*7 - 5

= 16 in (this is the width)