Question

The length of the sides of right angle triangle are (3x + 1)cm, (3x - 1)cm and X. Find the value of x.

Answer 1

Before knowing the vali we know side having 3x+1 cm is largest side.

So it is Hypotenuse.
By Pythagoras theorem ,
(3x+1)^2=x^2+(3x-1)^2
9x^2+6x+1=x^2+9x^2-6x+1
x^2-12x=9
x(x-12)=0
x=0 or 12
As side can't be 0 cm so 0 will be ignored.
so x = 12 cm

Answer 2

Given, Sides of the triangle :

Hypotenuse = (3x + 1)

Perpendicular = (3x - 1)

Base = x

We know that in a right angled ∆,

$\underline{\mathbf{{H}^{2} = {B}^{2} + {P}^{2}}}$

Putting the values we get,

${(3x + 1)}^{2} = {(x)}^{2} + {(3x - 1)}^{2} \\ \\ {(3x)}^{2} + {(1)}^{2} + 2 \times 1 \times 3x = {x}^{2} + {(3x)}^{2} + {(1)}^{2} - 2 \times 1 \times 3x \\ \\ 9 {x}^{2} + 1 + 6x = 9 {x}^{2} + 1 - 6x + {x}^{2} \\ \\ 6x = - 6x + {x}^{2} \\ \\ x(6) = x( - 6 + x) \\ \\ 6 = - 6 + x \\ \\ x = 6 + 6 \\ \\ \bf x = 12$

Hope it helps! ;)