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.
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.
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 = 2w + 2(2w)
60 = 6w
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 ft2