Question

The hypotenuse of a right angle triangle is 20 centimetre the difference between its other two sides is 4 centimetre find the length of its side

Answer 1

Answer:

one of the side is 12 cm while the other side is 16 cm.

Step-by-step explanation:

Let one of the sides be x then another side is 4 + x:

Applying Pythagoras theorem, we get::

(20)² = (x)² + (x + 4)²

400 = x² + x² + 8x + 16

400 = 2x² + 8x + 16

2x² + 8x - 384 = 0

x² + 4x - 192 = 0

x² + 16x - 12x - 192 = 0

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

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

x= 12 or x = -16

(But length can't be negative).

Hence, one of the side is 12 cm while the other side is:

one side = 4+x

other side = 4 + 12

                 = 16 cm.

So other side is 16 cm.

Verification::

(12)² + (16)² = 144 + 256 = 400

Hypotenuse = √400 = 20 cm

I hope it will helps you friend

Answer 2

Let the sides be x and x+4 .
According to Pythagoras theorem,
20*20=(x*x)+(x+4)*(x+4)
400= x^2 + x^2+8x+16
2x^2+8x-384=0
Taking 2 common,
x^2+4x-192=0
x^2+16x-12x-196=0
x(x+16)-12(x+16)=0
(x+16)(x-12)=0
Therefore, x=12cm
and other side=x+4=12+4=16cm