The length of a rectangle is
4 in longer than its width. If the perimeter of the rectangle is 48 in, find its area.
Now it's your turn.
I'll be glad to check your answer.
would I set it up like this:
48=4(4w+w)
?????
wait no... wouldn't it be 48+2(4w+w)???
48 equals 2(4w+w) not plus...
Close.
48 = 2(W + W + 4)
48 = 4W + 8
40 = 4W
10 = W
L = W + 4
P = 2 W + 2 L = 2 ( W + L ) = 48
2 ( W + W + 4 ) = 48
2 ( 2 W + 4 ) = 48 Divide both sides by 2
2 W + 4 = 24 Subtract 4 to both sides
2 W + 4 - 4 = 24 - 4
2 W = 20 Divide both sides by 2
W = 10 in
L = W + 4 = 10 + 4 = 14 in
A = L * W = 10 * 14 = 140 in ^ 2
To find the area of a rectangle, we need to know both its length and width. Let's label the width of the rectangle as "w" (in inches).
According to the problem, the length of the rectangle is 4 inches longer than its width. So, the length would be (w + 4) inches.
We are also given that the perimeter of the rectangle is 48 inches. The formula to calculate the perimeter of a rectangle is: Perimeter = 2 × (Length + Width).
Therefore, in equation form: 48 = 2 × (w + (w + 4)).
Simplifying the equation: 48 = 2 × (2w + 4).
Further simplifying: 48 = 4w + 8.
Now, let's solve for w:
Subtract 8 from both sides: 48 - 8 = 4w.
40 = 4w.
Divide both sides by 4: w = 10.
So, the width of the rectangle is 10 inches.
Now we can find the length by substituting the value of the width into our expression for length: length = w + 4 = 10 + 4 = 14 inches.
To find the area of the rectangle, we multiply the length by the width: Area = length × width = 14 × 10 = 140 square inches.
Therefore, the area of the rectangle is 140 square inches.