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Question 53
The perimeter of a rectangular table is 60 cm. If the area of the rectangular table is 209 $$cm^2$$, then what will be the length of the table?
Solution
Let Length of the rectangle = l cm
Breadth of the rectangle = b cm
Given, 2(l+b) = 60 => l+b = 30
=> b = 30-l
Given, lb = 209
Substituting b = 30-l in above equation,
l(30-l) = 209
=> $$30l-l^2 = 209$$
=> $$l^2 - 30l+209 = 0$$
$$l^2 - 11l - 19l+209 = 0$$
=> $$l(l-11)-19(l-11) = 0$$
=> $$(l-11)(l-19) = 0$$
l = 11 or l = 19
Therefore, Length of the rectangle can be 11 cm or 19 cm
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