the perimeter of a rectangle is 228 inches. the length exceeds the width by 76 inches. find the length and the width.
P = 2L + 2W
228 = 2(W + 76) + 2W
228 = 4W + 152
228 - 152 = 4W
76 = 4W
19 = W
L = 19 + 76 = 95
Check it out:
228 = 2(95) + 2 (19)
228 = 190 + 38
238 = 238
228 = 228
To find the length and width of the rectangle, we can set up a system of equations based on the information given.
Let's assume the width of the rectangle is "w" inches. Since the length exceeds the width by 76 inches, the length can be represented as "w + 76" inches.
The perimeter of a rectangle is given by the formula: perimeter = 2(length + width).
According to the problem, the perimeter is 228 inches. We can now write the equation:
228 = 2(w + 76 + w)
Simplifying the equation:
228 = 2(2w + 76)
228 = 4w + 152
228 - 152 = 4w
76 = 4w
w = 76 / 4
w = 19
Now that we have the width, we can find the length by substituting the value of the width back into the equation for the length:
Length = Width + 76
Length = 19 + 76
Length = 95
Therefore, the width of the rectangle is 19 inches, and the length is 95 inches.