Rectangle Ratio Calculation
We are given the ratio of the length (L) to the perimeter (P) of a rectangle:
$ \frac{L}{P} = \frac{3}{20} $
Let the length be $ L = 3x $ and the perimeter be $ P = 20x $ for some positive value $ x $.
Finding Breadth from Perimeter
The formula for the perimeter of a rectangle is:
$ P = 2(L + B) $
Where $ B $ represents the breadth.
Substitute the values $ P = 20x $ and $ L = 3x $ into the formula:
$ 20x = 2(3x + B) $
Solving for Length to Breadth Ratio
Divide both sides by 2:
$ 10x = 3x + B $
Isolate the breadth $ B $:
$ B = 10x - 3x $
$ B = 7x $
Now, find the ratio of length to breadth ($ L : B $):
$ L : B = 3x : 7x $
Simplify the ratio by dividing both parts by $ x $:
$ L : B = 3 : 7 $
Therefore, the length and breadth are in the ratio of 3 : 7.
Similar Questions
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Important Questions from 2-D Mensuration
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