The rectangle shown has a perimeter of 80 cm and the given area. Its length is 4 more than three times its width. Write and solve a system of equations to find the dimensions of the rectangle.

Question

I would like to know the length and width of the rectangle. The area is 279cm2. (2 is supposed to be an exponent) Please help!

Answer 1

Here are the steps you need to take to derive the answer..

1. Write the perimeter equation in terms of L and W of the rectangle,
2. Write the relationship between L and W as given

2.L + 2.W = 80

L = 3W + 4

Solve this system of equations by substitution. You should get

L = 31cm

W= 9 cm

Answer 2

A=LW=279

Perimeter=2L+2W=80

L=4+3W

Substitute L=4+3W into the Perimeter equation 2(4+3W)+2W=80. Solve for W

8+6W+2W=80 8W=80-8 divide by 8, W=10-1=9 L=4+3W = 4+3(9)=4+27=31

L=31, W=9 Area = LW=31x9=279