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23. The hypotenuse of a grassy land in the shape of a right triangle is 1 metre more thanwird side is 7 metres more than the shortest side, find the sides of the grassyland. |
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Answer» Let shortest side of right triangle be xThen, hypotenuse h = 2x + 1Third side y = x + 7 Using pythagoras theoram,h^2 = x^2 + y^2Put value of h and y(2x + 1)^2 = x^2 + (x + 7)^24x^2 + 1 + 4x = x^2 + x^2 + 49 + 14x4x^2 - 2x^2 + 4x - 14x + 1 - 49 = 02x^2 - 10x - 48 = 0x^2 - 5x - 24 = 0x^2 + 8x - 3x - 24 = 0x(x + 8) - 3(x + 8) = 0(x - 3)(x + 8) = 0x = 3, - 8 Negative value not possible Therefore,Sides of grassy land areShortest side = x = 3 mHypotenuse = 2x + 1 = 2*3 + 1 = 7 mThird side = x + 7 = 10 m |
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