Question

Solve for x.

The length of a rectangle is equal to 2 times the width plus 3 feet. If the area of the rectangle is 20 square feet, what are the dimension of the rectangle?

Answer 1

let width be x feet
then the length = 2x + 3 feet

then the area = x(2x + 3) = 20

2x^2 + 3x - 20 = 0

(2x - 5)(x + 4) = 0

x = 2.5 or -4 ( ignore the negative value)

so the deimnasions are width = 2.5 feet and length = 2(2.5) + 3 = 8 feet

Answer 2

l*w=20, so l=20/w
l=2w+3

20/w=2w+3
20=2w^2+3w
2w^2+3w-20=0

Slip and slide
w^2+3w-40
(w+8)(w-5)
(w+8/2)(w-5/2)
(w+4)(2w-5)

w= -4 or 5/2, but since width must be positive, it is 5/2

(5/2)*l=20
l=8

Final answer: Length= 8, Width= 5/2