Question

the hypotenuse of a right angled triangle is 6 m mote than twice of the shortest side.the third side is two meters less thanthe hypotenuse than the hypotenuse. represent the above situation into algebrically equations​

Answer 1

Answer:

If shortest side = x

Hypotenuse = 2x + 6

Third side = 2x + 4

(Only for this question)

I have also found out the value of x in EXTRA.

Step-by-step explanation:

Let shortest side be x m.

Acc. to ques,

Hypotenuse = 6 m more than twice of the shortest side

=> (2x + 6) m

Third side = Hypotenuse - 2

=> (2x + 6) - 2 => (2x + 4) m

EXTRA:

As triangle is right-angled, by Pythagoras' theorem,

x² + (2x + 4)² = (2x + 6)²

=> x² + 4x² + 16x + 16 = 4x² + 24x + 36

=> x² - 8x - 20 = 0

=> x² + 2x - 10x - 20 = 0

=> x(x + 2) - 10(x + 2) = 0

=> (x + 2)(x - 10) = 0

∴ x = -2 or 10

As sides cannot be negative, x = 10 m

Thus, shortest side = x = 10m

Hypotenuse = 2x + 6 => 2(10) + 6 => 20 + 6 => 26 m

Third side = 2x + 4 => 2(10) + 4 => 20 + 4 => 24 m