I need to know the answer to this question. The length of a rectangle is twice its width. The perimeter is 60ft. What is the area. Please explain in complete sentences the steps necessary to find the area.

## The length of a rectangle is twice its width. The perimeter is 60ft.. Find the area. Explain in complete sentences the steps necessary to find the area.

# 2 Answers

Set the following: Length = L Width = W

The length is twice the width: L = 2*W or: W = L/2

Perimeter: P = 60ft = 2*L + 2*W

Substituting L for W in the perimeter equation gives:

P = 60ft = 2*L + 2*(L/2) = 2*L + L = 3L

L = 60ft/3 = 20ft W=L/2=20ft/2=10ft

Verify result: Perimeter= P = 60ft = 2L + 2W = 2*20ft +2*10ft = 40ft+20ft = 60ft

The area of the rectangular is: Area = A = Length*Width = L*W = 20ft*10ft = 200 (ft)^2

Since the statement, "the **length is twice its width**" puts one dimension in terms of the other it's easiest to use "w" as the variable.

So,

**w** = **width**

**2w** =** length**

The perimeter is the sum off all the sides of the rectangle

P = w + w + l + l = 2w + 2l

Using our terms and the value of 60, substitute them into the equation.

60 = 2**w** + 2**(2w)**

60 = 6**w**

**w = 10 ft**

**l = 2w = 20 ft**

**Checking our solution:
**

**60 ft = 10 ft + 10 ft + 20 ft + 20 ft
**

**60 ft = 60 ft
**

Now onto the area, the area of a rectangle is the product of its dimensions and is given by the formula

**Area = l*w**

substituting our values in from above

A = (20 ft)*(10 ft) =** 200 ft ^{2}**