The area of a rectangular piece of cardboard is 90 square centimeters, and the perimeter is 46 centimeters. How do you find the dimensions of the rectangle?

1 Answer
Nov 14, 2016

Please see the explanation.

Explanation:

Let L = the length

Let W = the width

LW = 90" cm"^2" [1]"

2L + 2W = 46" cm [2]"

Divide equation [2] by 2:

L + W = 23" cm"

Subtract L from both sides:

W = 23" cm" - L

Substitute 23" cm" - L for W in equation [1]:

L(23" cm" - L) = 90" cm"^2

Use the distributive property

23" cm"(L) - L^2 = 90" cm"^2

Subtract 90" cm"^2 from both sides:

23" cm"(L) - L^2 - 90" cm"^2 = 0

Multiply both sides by -1:

L^2 - 23" cm"(L) + 90" cm"^2 = 0

Having solved this type of problem with the quadratic formula, many times, I know that the greater of the two solutions gives the length and the lesser, the width:

L = (23" cm" + sqrt((23" cm")^2 - 4(1)(90" cm"^2)))/2

L = 18" cm"

W = (23" cm" - sqrt((23" cm")^2 - 4(1)(90" cm"^2)))/2

W = 5" cm"