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The length of a rectangle is 13 centimeters less than three times its width. Its area is 56 square centimeters. Find the dimensions of the r
Question
The length of a rectangle is 13 centimeters less than three times its width. Its area is 56 square centimeters. Find the dimensions of the rectangle. Use the formula, area=length*width.
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Mathematics
6 months
2021-07-19T08:45:57+00:00
2021-07-19T08:45:57+00:00 2 Answers
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Answers ( )
Answer:
The dimensions of the rectangle are 8 by 7 centimeters.
Step-by-step explanation:
The length of a rectangle is 13 centimeters less than three times its width. In other words:
Given that the area of the rectangle is 56 square centimeters, we want to determine its dimensions.
Recall that the area of a rectangle is given by:
Substitute in known values and equations:
Solve for w. Distribute:
Isolate the equation:
Factor. We want to find two numbers that multiply to 3(-56) = -168 and that add to -13.
-21 and 8 suffice. Hence:
Zero Product Property:
Solve for each case:
Since the width cannot be negative, we can ignore the first solution.
Therefore, the width of the rectangle is seven centimeters.
Thus, the length will be:
Thus, the dimensions of the rectangle are 8 by 7 centimeters.
Answer:
Area = length x width
Area = (3width – 13) x width
Area = 3 width^2 -13width
56 = 3width^2 -13 width
Width = 7
Length = (3 *7) -13 = 8
Step-by-step explanation: