The area of a rectangle is 12 square inches. The length is 5 more than twice the width. Find the length and width

Let the width of the triangle be x.

Therefore length = 2x + 5. (5 more than twice its width).

Area = L * W = (2x + 5) x = 12.

2x^2 + 5x = 12

2x^2 + 5x - 12 = 0.

This is a quadratic equation. (2) * (-12) = - 24.

We think of two numbers whose product is - 24 and it sum is + 5.

Those two numbers are 8 and - 3. So we replace the middle term of

quadratic with (8 - 3).

2x^2 + 5x - 12 = 0.

2x^2 + 8x-3x - 12 = 0. Factorize.

2x (x + 4) - 3 (x + 4) = 0

(2x-3) (x+4) = 0.

(2x-3) = 0 or (x+4) = 0

2x = 3. x = 0 - 4

x = 3/2 = 1.5 x = - 4. (x can't be negative, since we are solving for lengths)

x = 1.5 is only valid solution.

width = x = 1.5

Length = (2x + 5) = 2*1.5 + 5 = 3 + 5 = 8.

Therefore length = 8, and width = 1.5

Cheers.