Question

The hypotenuse of a right triangle is 20 m. if the difference between the lengths of other sides be 4m, find the other sides​

Answer 1

Answer:

16 and 12

Step-by-step explanation:

16²=256

12²=144

----------------

20²=400

and 16-12=4

Answer 2

Answer

Let the one side be x

the another side be (x+4)

By Pythagoras Theorem

$(20)^2 = (x)^2 + (x + 4)^2$

=> $400 = x^2 + x^2 + 8x + 16$

=> $400 = 2x^2 + 8x + 16$

=> $2x^2+ 8x + 16-400 = 0$

=> $2x^2 + 8x - 384 = 0$

=> $2(x^2 + 4x - 192) = 0$

=> $x^2 + 4x - 192 = 0$

=> $x^2 + 16x - 12x - 192 = 0$

=> $x(x + 16) - 12(x + 16) = 0$

=> $(x - 12)(x + 16) = 0$

=> $x= 12 or x = -16 (Neglected)$

As Length cannot be so it is neglected

SO

So one  side is 12 cm and the other is 16 cm

Verification

$(12)^2 + (16)^2 = 144 + 256 = 400$

=> $Hypotenuse = \sqrt{400}  = 20 cm$