Question

The length of Joseph’s rectangular poster is two times it’s width. If the perimeter is 24 inches, what is the area of the poster?

Answer 1

The area of poster is 32 square inches

Solution:

Let "a" be the length of rectangle

Let "b" be the width of rectangle

The length of Joseph’s rectangular poster is two times it’s width

Therefore,

Length = 2 times width

a = 2b --------- eqn 1

The perimeter is 24 inches

The perimeter of rectangle is given by formula:

$Perimeter = 2(length+width)$

Substituting the given values we get,

$24 = 2(2b + b)\\\\24 = 2(3b)\\\\\text{Divide both sides of equation by 2 }\\\\12 = 3b\\\\\text{Divide both sides of equation by 3}\\\\b = 4$

Substitute b = 4 in eqn 1

a = 2(4)

a = 8

Thus we got,

Length = 8 inches

Width = 4 inches

The area of rectangle is given by formula:

$Area = length \times width\\\\Area = 8 \times 4\\\\Area = 32$

Thus area of poster is 32 square inches