Question
There is a rectangular paper, whose length and breadth
are in the ratio 12:11, respectively and it has a perimeter of 92 metres. If a triangular piece with height of 9 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 β12xβ metres and β11xβ metres, respectively Then, perimeter of the paper = 2 Γ (length + breadth) = 2 Γ (12x + 11x) = 46 x metres So, 46x = 92 So, x = (92/46) = 2 So, area of the entire paper = length Γ breadth = (12 Γ 2) Γ (11 Γ 2) = 24 Γ 22 = 528 m2 Area of the triangular piece = (1/2) Γ base Γ height = (1/2) Γ 9 Γ 10 = 45 m2 So, area of the remaining paper = 528 β 45 = 483 m2
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