the length of a rectangle is 2 inches more than its width . if the are is 48 square inches, what is the length

Answer 1

Greetings! Lets solve this shall we ?

So let the length be l = x + 2, the width be w = x and the Area be 48 in². Lets solve for the length!

So the Area formula of a Rectangle is A = length times width (A=l*w) and we use this to find the x-value for the length! Then,

x(x+2) = 48 representing l*w = w*l = A. We distribute the x inside to get

x²+2x = 48.....................Then we subtract 48 to both sides obtaining a quadratic equation to factor

x²+2x-48 = 0 ..............We notice this factors into

(x+8)(x-6) = 0..............We solve each x value using the Zero-Product Property such that

x + 8 = 0 and x - 6 = 0............Then

x = -8 and x = 6...............We cannot have negative width so we rule out -8 and use 6 to find the length

length = x + 2 = (6) + 2 = 8 inches!

I hope this helped!