Question 618648: the ratio of two sides of a parallelogram is 3.5 and its perimeter is 48 cm . find the sides of the pallelogram. Answer by math-vortex(648) (Show Source):
You can put this solution on YOUR website! Hi, there--
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Recall that a parallelogram has two pairs of parallel sides. We will use two variables to solve this problem.
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Let x be the length of each of the shorter pair of parallel sides.
Let y be the length of each of the longer pair of parallel sides.
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We will use the information given in the problem to write two equations that model the problem. The perimeter (48 cm.) is the sum of the four sides, so
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The ratio of two sides of the parallelogram is 3.5. Since the parallel sides of a parallelogram have equal length, we know that we are comparing the lengths x and y here, so
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NOTE: We set up the variable so that y is longer than x. The ratio is greater than 1 so we know that we are comparing the longer side to the shorter one.
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Now we have two variables and two equations. We can solve the system to find the values of x and y.
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Rewrite the first equation in terms of x.
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Substitute 24-x for y in the second equation.
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Solve for x.
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I'm not a fan of decimal coefficients, so I multiply every term by 2.
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We now know that the shorter sides have a length of 16/3 cm. Substitute 16/3 for x in the first equation.
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According to this equation, the length of the longer side is 56/3 cm.
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Now we side to check our work. The perimeter is 48 cm.
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The perimeter checks out. Now we need to check that the ratio of the two sides reduces to 3.5.
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Check! So the lengths of the sides of the parallelogram are 16/3 cm and 56/3 cm.
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Hope this helps. Feel free to email me if you have questions about this.
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Ms.Figgy
math.in.the.vortex@gmail.com
