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Question
A carpet of size 5 m × 2 m has 25 cm wide red border. The inner part of the carpet is blue in colour (see figure). Find the area of blue portion. What is the ratio of areas of red portion to blue portion?
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Solution
Given, size of carpet = 5 m × 2 m and width of border = 25 cm = `25/100` × m = 0.25 m
∴ Area of carpet ABCD = AB × BC = 5 × 2 = 10 m2 ...[∵ Area of rectangle = Length × breadth]
So, length of inner blue portion, EF = AB – (2 × 0.25 cm) = 5 – 0.50 = 4.5 m
And breadth of inner blue portion FG = BC – (2 × 0.25) = 2 – 0.50 = 1.5 m
Area of blue portion = Area of rectangle EFGH = EF × FG = 4.5 × 1.5 = 6.75 m2
Now, area of red portion = Area of ABCD – Area of EFGH = 10 – 6.75 = 3.25 m2
∴ Ratio of areas of red portion to blue portion = 3.25 : 6.75 = 13 : 27
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