A rectangular piece of cardboard has a perimeter of 88 cm. The length of the rectangle is 8 cm longer than three times the width. Find the length and width of the rectangle.
To solve this problem, we can use the information given to set up equations and find the values of the length and width of the rectangle.
Let's start by assigning variables to the length and width of the rectangle. Let's say the width is "w" cm.
According to the given information, the length of the rectangle is 8 cm longer than three times the width. This can be written as "length = 3w + 8".
The perimeter of a rectangle is calculated by adding all four sides. So, we can set up an equation using the perimeter:
Perimeter = 2(length + width)
Substituting the given values, we get:
88 = 2(3w + 8 + w)
Now, we can simplify the equation to solve for the width:
88 = 2(4w + 8)
44 = 4w + 8
36 = 4w
w = 9
Now that we have the width (w = 9), we can find the length by substituting this value into our equation for the length:
length = 3w + 8
length = 3(9) + 8
length = 27 + 8
length = 35
Therefore, the length of the rectangle is 35 cm and the width is 9 cm.
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P = 2L + 2W
88 = 2(3W + 8) + 2W
88 = 8W + 16
72 = 8W
9 = W