Question

Thehypotenuse of a right angle triangle is 20 cm. The difference between its other two is 4cm. Find the length of the side

Answer 1

A.P.Q.

Hypotenuse=20cm
Let the other two sides be X and 4+X

Now, by Pythagoras theorem

${20}^{2 } = {x}^{2} + ({4 + x}) ^{2} \\ 400 = {x}^{2} + 16 + {x}^{2} + 8 x \\ {2x}^{2} + 8x - 384 = 0 \\ taking \: 2 \: common \\ {x }^{2} + 4x - 192 = 0 \\ {x}^{2} + 16x - 12 x - 192 = 0 \\ x(x + 16) - 12(x + 16) = 0 \\ so \: x = - 16 \: and \: 12 \\ - 16 \: will \: be \: rejected \\ so \: x = 12$
So, sides of triangle will be 12 and 16.