Question
There is a rectangular paper, whose length and breadth
are in the ratio 5:4, respectively and it has a perimeter of 90 metres. If a triangular piece with height of 11 metres and base of 12 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 ‘5x’ metres and ‘6x’ metres, respectively Then, perimeter of the paper = 2 × (length + breadth) = 2 × (5x + 4x) = 18 x metres So, 18x = 90 So, x = (90/18) = 5 So, area of the entire paper = length × breadth = (5 × 5) × (4 × 5) = 25 × 20 = 500 m2 Area of the triangular piece = (1/2) × base × height = (1/2) × 11 × 12 = 66 m2 So, area of the remaining paper = 500 – 66 = 434 m2
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