Question

a folded napkin has a triangular cross section of sides x cm ,x +1 cm and x+2 cm if one of the angles of the triangle is 90 degrees find x​

Answer 1

The value of x is 3 cm.

Step-by-step explanation:

Given : A folded napkin has a triangular cross section of sides x cm, x +1 cm and x+2 cm if one of the angles of the triangle is 90 degrees.

To find : The value of x ?

Solution :

One of the angle is ​90 degrees i.e. it is a right angled triangle.

Applying Pythagorean theorem,

$H^2=P^2+B^2$

Where, H is the hypotenuse the largest side i.e. H=x+2 cm

P is the perpendicular i.e. P=x+1 cm

B is the perpendicular i.e. B=x cm

Substitute the value,

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

$x^2+ 4x + 4 = x^2+ x^2+ 2x + 1$

$x^2+ 4x + 4 = 2x^2+ 2x + 1$

$2x^2- x^2+ 2x - 4x + 1 - 4 = 0$

$x^2- 2x - 3 = 0$

$x^2- 3x + x - 3= 0$

$x(x-3) + 1(x-3) = 0$

$(x-3)(x + 1) = 0$

$x = 3,-1$

Reject x=-1 as it is not possible.

So, x=3

The sides are 3,4,5 cm.

Therefore, the value of x is 3 cm.