Question

if the sides of a right angled triangle are x,x+1,x-1 then the hypotenuse is ______

Answer 1

Here,
Side 1 --- x
Side 2 --- x+1
Side 3 ----x-1


According to the Pythagoras theorem, we have

$(side1) {}^{2} + (side2) {}^{2} = (side3) {}^{2}$
=>
$x {}^{2} +(x - 1) {}^{2} = (x + 1) {}^{2}$

Answer 2

Answer:

if the sides of a right angled triangle are x,x+1,x-1 then the hypotenuse is 5 .

Step-by-step explanation:

Explanation:

As we know that, in right angle triangle hypotenuse is the largest size.

So, hypotenuse = (x + 1) , base = x and perpendicular = x- 1

Step 1:

By Pythagoras theorem,

$(x+1)^2 = x^2 + (x- 1)^2$

⇒$(x^2 + 2x + 1) = x^2 + (x^2 - 2x + 1)$

⇒ $(2x^2 - x^2 -2x -2x +1 - 1 )$ = 0

⇒$x^2 = 4x$

⇒ x = 4

Therefore, the length of hypotenuse = x + 1 = 4 + 1 = 5 units.

Final answer:

Hence, the hypotenuse is 5 units.

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