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Question 53
The ratio between the perimeter and the breadth of a rectangle is 3 : 1. If the area of the rectangle is 310 sq. cm, the length of the rectangle is nearly:
Solution
Let the length and breath of the rectangle be l cm and b cm
Given, $$\dfrac{2(l+b)}{b} = \dfrac{3}{1}$$
=> 2(l+b) = 3b
=> 2l+2b = 3b
=> b = 2l
Given, lb = 310
Substituting b = 2l in above equation
$$l\times 2l = 310$$
$$2l^2 = 310$$
=> $$l^2 = 155$$
We know that $$12^2 = 144$$ and $$13^2 = 169$$.Â
Hence, The value of l lies in between 12 and 13.
Therefore, From the options, l = 12.45 cm
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