The perimeter of a rectangle is 30 inches and its area is 54 square inches. How do you find the length of the longest side of the rectangle?
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perimeter of rectangle = 30 inche
......... 2(l + b) = 30
l+b = 30/2 = 15
l+ b = 15.
l= 15-b. ......(1)
area of rectangle = 54 sq inches
area =l×b =54 sq inches.....(2)
put value of l from (1) to (2)
so, l×b = 54
(15-b)×b = 54
15b - b^2 = 54
=> b^2 -15b +54 = 0
=> b^2 - 9b-6b + 54= 0
=> b(b-9) -6(b-9) = 0
=> (b-6)(b-9) = 0
=> b= 6 ,b=9
put this value in (1)
when b = 6 inch
then l= 15-6=9 inch
when b = 9 inch
then l= 15-9= 6 inch
so , longest side of rectangle is 9 inch
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