Question

The rectangle shown has a perimeter of 96 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.

Answer 1

Explanation:

formulas you need to know off the top of your head.

P = 2*L + 2*W

A= L*W

plug in what we are given

96 = 2*L + 2*W

407 = L*W

we are also given this.

L =3*W+4

There are two methods for solving this, the substitution method or the elimination method. Both work well, and it's more of an choice of which method you prefer.

In our given problem, elimination method on the top two equations would get rid of both the L and the W, so let's go for the substitution method.

let's substitute in L , from the 3rd equation into L of the 1st equation

96 = 2(3*W+4 ) +2W

96 = 6W +8 +2W

96 -8 = 8W

88 = 8W

11 =W

Nice ! now we've got W

use the 2nd equation with our found value for W

407 = L * 11

37 = L

nice now we have both dimensions :)

Answer 2

• 11 cm and 37 cm

--------------------------------

Given rectangle with

• P = 96 cm,
• L = 3W + 4.

Find the dimensions

Use perimeter formula

• P = 2(L + W)
• 96 = 2(L + W)
• 48 = L + W

Substitute L = 3W + 4

• 48 = 3W + 4 + W
• 48 - 4 = 4W
• 44 = 4W
• W = 44/4
• W = 11

Find L

• L = 3*11 + 4 = 37