Length and width

Question

The rectangle shown has a perimeter of 130 cm and the given area. It’s length is 5 more that five times it’s width. Write and solve a system of equations to find the dimensions of the rectangle

Answer 1

Length = 55

Width = 10

We have two equations

P = 2L + 2W

L = 5W + 5

130 = 2L + 2W

We can divide both sides by 2

65 = L + W = Equation 1

5 = L - 5W = Equation 2

We can eliminate W if we multiply Equation 1 by 5

325 = 5L + 5W

5 = L - 5W

Combininig we have

330 = 6L

Divide both sides by 6

55 = L

65 = 55 + W

Subtract 55 from both sides

65 - 55 = W

10 = W

Checking

L = 5W + 5 = 5(10) + 5 = 50 + 5 = 55

130 = 2L + 2W

130 = 2(55) + 2(10)

130 = 110 + 20

130 = 130

Of course substitution can be used and 5W + 5 = 65 - W can be used to solve for W since both are equal to L.