the length of a rectangle is 1 inch greater than its width if its dimensions are doubled its area increases by 36 square inches give an equation to find its dimensions

original width -- x

original length -- x+1
original area = x(x+1)

new width --- 2x
new length --- 2x+2
newarea = 2x(2x+2)

2x(2x+2) - x(x+1) = 36
4x^2 + 4x - x^2 - x - 36=0
3x^2 + 3x - 36 = 0
x^2 + x - 12=0
(x+4)(x-3) = 0
x = 3 or x = -4, the latter is silly answer

original width = 3, length = 4
new width = 6, new length = 8

check:
old area = 12
new area = 48
for an increase of 36
Answer is correct!