The perimeter of a rectangle is 56 inches. The length exceeds the width by 24 inches. What is the length and what is the width?
P = 2L + 2W
56 = 2(W + 24) + 2W
56 = 2W + 48 + 2W
56 = 4W + 48
8 = 4W
2 = W
Width = W INCHES., Length = (w + 24 )in
2W + 2(W+24) = 56,
2W + 2W + 48 = 56,
4W + 48 = 56,
4W = 8,
W E 2 in = Width.
W + 24 = 2 + 24 = 26 in = Length.
To find the length and width of a rectangle given the perimeter and the length-width relationship, you can set up a system of equations.
Let's denote the length of the rectangle as L and the width as W.
According to the problem, the perimeter of the rectangle is 56 inches. The formula for the perimeter of a rectangle is given by:
Perimeter = 2(L + W)
Substituting the given perimeter into the equation, we have:
56 = 2(L + W)
Simplifying the equation, we divide both sides by 2:
28 = L + W
We also know that the length exceeds the width by 24 inches. Mathematically, this can be expressed as:
L = W + 24
Now we can substitute this into the equation we derived from the perimeter:
28 = (W + 24) + W
Simplifying further, we combine like terms:
28 = 2W + 24
To isolate W, we subtract 24 from both sides:
28 - 24 = 2W
4 = 2W
Finally, divide both sides by 2:
2 = W
Therefore, the width of the rectangle is 2 inches.
To find the length, we substitute this value of W back into the equation we derived earlier:
L = W + 24
L = 2 + 24
L = 26
Therefore, the length of the rectangle is 26 inches.
In summary, the length of the rectangle is 26 inches and the width is 2 inches.