The length of a rectangle is 3 more than twice the width. The area of the rectangle is 119 square inches. What are the dimensions of the rectangle

What we know:
Area: 119 sq inches
Length (l) = 2w + 3

Area: l • w
119 = l x w
119 = (2w + 3) x w /// I plugged in l as (2w+3)
119 = 2w^2 + 3w
0 = 2w^2 + 3w - 119

a = 2
b = 3
c = -119

Use the quadratic formula

w = -b+/-√(b^2 - 4ac)
—————————
2(a)

(Sorry if this equation looks weird you can find it on the internet by searching quadratic formula)

w = -3 +/- √(9 - 4(2)(-119)
——————————-
(2)2

w = -3 +/- √(9 + 952)
——————————-
4

w = -3 +/- √(961)
——————
4

w = -3 +/- 31
—————
4
(It cannot be -31 since there is no negative measurement so it is +31)

w = -3 + 31
————
4

w = 28
—
4

w = 7 units
l = w + 3
l = 10 units

The range would be 13 because you’re finding the difference