Respuesta :
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,
[tex]H^2=P^2+B^2[/tex]
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,
[tex](x+2)^2 = x^2+ (x+1)^2[/tex]
[tex]x^2+ 4x + 4 = x^2+ x^2+ 2x + 1[/tex]
[tex]x^2+ 4x + 4 = 2x^2+ 2x + 1[/tex]
[tex]2x^2- x^2+ 2x - 4x + 1 - 4 = 0[/tex]
[tex]x^2- 2x - 3 = 0[/tex]
[tex]x^2- 3x + x - 3= 0[/tex]
[tex]x(x-3) + 1(x-3) = 0[/tex]
[tex](x-3)(x + 1) = 0[/tex]
[tex]x = 3,-1[/tex]
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.
You can use the fact that sides of a right angled triangle follows Pythagoras theorem.
The value of x is 3 cm
What is Pythagoras theorem?
If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]
How to find the value of x for given condition?
Since there is one angle as 90 degrees in the triangle cross section by napkin, thus, it is a right angled triangle and its sides will follow Pythagoras theorem.
It is a fact that the hypotenuse of a right angled triangle is the biggest side and that all sides of a triangle are positive.
Since x is one of the side, thus x > 0 and thus, x + 2 is the biggest side, and thus, being hypotenuse.
From Pythagoras theorem, we have:
[tex](x+2)^2 = x^2 + (x+1)^2\\x^2 + 4 + 4x = x^2 + x^2 + 1 + 2x\\x^2 - 2x - 3 = 0\\x^2 - 3x + x - 3 = 0\\x(x-3) + 1(x-3) = 0\\(x+1)(x-3) = 0\\x = -1, 3[/tex]
Since x is a side of a triangle, thus x needs to be positive, thus, x = 3 cm is the answer.
Thus,
The value of x is 3 cm
Learn more about right angled triangles here:
https://brainly.com/question/4456796
