Question

in a right angle triangle, length of the hypotenuse is 6cm more than it's shortest side. the length of the other side is 3cm less than the Hypotenuse,then find the sides of right angle triangle​

Answer 1

Answer:

9cm,12cm and15cm

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Answer 2

let the length of shortest side be x cm

then , hypotenuse = x + 6 cm

then , length of other side = x + 3 cm

By Pythagoras therom,

${h}^{2} = {s}^{2} + {s}^{2}$

substitute all the values , we get

${(x + 6)}^{2} = {x}^{2} + {(x + 3)}^{2}$

${x}^{2} + 36 + 12x = {x}^{2} + {x }^{2} + 6x + 9$

${x}^{2} + 12x + 36 = 2x ^{2} + 6x + 9$

$2 {x}^{2} + 6x + 9 - {x}^{2} - 12x - 36 = 0$

${x}^{2} - 6x - 27 = 0$

${x}^{2} + 3x - 9x - 27 = 0$

$x(x + 3) - 9(x + 3) = 0$

$(x + 3)(x - 9) = 0$

$x = - 3 \: \: or \: \: 9$

We know that, side never be negative.

So , x = 9

Shortest side = 9 cm

other side = 12 cm

Hypotenuse = 15 cm

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