The length of a rectangle is 4 more than twice the width. If the perimeter of the rectangle is 104 centimeters, what are the length and width of the rectangle? please helpp
Mathematics · High School · Tue Nov 03 2020
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Given the statement:
The length of a rectangle is 4 more than twice the width.
Determine the length and width of the rectangle if the perimeter is 104 centimeters.
Solution:
P = 104 cm
Let w = width of the rectangle
Let l = 4 + 2w
Formula for the perimeter of the rectangle:
P = 2w + 2l
Substitute the given representation of w and l and the value of P in the formula.
104 = 2(4) + 2(4+2w)
104 = 8 + 8 + 4w
104 = 16 +4w
transpose 16 on the other side of the equation, note that when transposing a number, the sign changes.
104 - 16 = 4w
88 = 4w
Divide both sides by 4 in order to find the value of w.
w = 22
Find the value of the length of the rectangle by substituting the value of the value of the width.
l = 4 + 2(22)
l = 48
Final answer:
Width = 22 cm
Length = 48 cm