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The lengths of the largest side of a qua...

The lengths of the largest side of a quadrilateral is three times that of its smallest side. Out of the other two sides length of one is twice that of the smallest and the other is 1 cm. longer than the smallest. If the perimeter of the quadrilateral is at most 36 cm. then find the maximum possible lengths of its sides.

Text Solution

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Let the smallest side = x cm
Largest side = 3x cm
Other two sides are 2x cm and x + 1 cm.
`rArr The perimeter = x + 3x + 2x + x + 1
7x + 1 cm
According to the question
7x + 1 le 36
`rArr 7x le 35
`rArr x le 5`
Maximum value of x = 5
`therefore` The maximum possible length of sides are x = 5 cm , 3x = 15 cm , 2x = 10 cm and x + 1 = 6 cm.
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