Question
There is a rectangular paper, whose length and breadth
are in the ratio 6:7, respectively and it has a perimeter of 78 metres. If a triangular piece with height of 14 metres and base of 10 metres is cut out from the given paper then find the area (in m2) of the remaining paper.Solution
Let the length and breadth of the rectangular be ‘6x’ metres and ‘7x’ metres, respectively Then, perimeter of the paper = 2 × (length + breadth) = 2 × (6x + 7x) = 26 x metres So, 26x = 78 So, x = (78/26) = 3 So, area of the entire paper = length × breadth = (6 × 3) × (7 × 3) = 18 × 21 = 378 m2 Area of the triangular piece = (1/2) × base × height = (1/2) × 14 × 10 = 70 m2 So, area of the remaining paper = 378 – 70 = 308 m2
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