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Class 10 > Learn Mathematics > The hypotenuse of a grassy land in the shape of right...
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The hypotenuse of a grassy land in the shape of right triangle is 1 meter more than twice the shortest side. If the third side is 7 meters more than the shortest side, find the sides of the grassy land?

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Let the length of the shortest side be x. Then, the two sides other than the hypotenuse are x and (x + 7). So, by the given condition: (2x +1)^2 = x^2 + (x + 7)^2.
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Let the length of the shortest side be x. Then, the two sides other than the hypotenuse are x and (x + 7). So, by the given condition: (2x +1)^2 = x^2 + (x + 7)^2 => 4x^2 + 4x + 1=2x^2 + 14x + 49=> 2x^2 -10x - 48=0 => x^2 - 5x - 24=0 => x^2 - 8x + 3x -24 = 0=> (x - 8)(x + 3) = 0 x = 8 or -...
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Let the length of the shortest side be x. Then, the two sides other than the hypotenuse are x and (x + 7). So, by the given condition: (2x +1)^2 = x^2 + (x + 7)^2 => 4x^2 + 4x + 1=2x^2 + 14x + 49=> 2x^2 -10x - 48=0 => x^2 - 5x - 24=0 => x^2 - 8x + 3x -24 = 0=> (x - 8)(x + 3) = 0 x = 8 or - 3. But the length of a side of a land cannot be negative. So, x = 8m and the other sides are x + 7 = 15m, and (2x + 1) = 17m. So, the sides of the land are 8m, 15m, and 17m. read less
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