The length of the sides of a right angled triangle are xcm, 2x-1, 2x+1. Find x
Let's use the Pythagorean theorem to solve for x.
According to the Pythagorean theorem, the sum of the squares of the two shorter sides of a right-angled triangle is equal to the square of the length of the hypotenuse.
So, we have:
x^2 + (2x-1)^2 = (2x+1)^2
Expanding the terms gives us:
x^2 + 4x^2 - 4x + 1 = 4x^2 + 4x + 1
Combining like terms gives us:
5x^2 - 4x + 1 = 4x^2 + 4x + 1
Subtracting 4x^2 and 1 from both sides gives us:
x^2 - 8x =0
Factoring out an x gives us:
x(x-8) = 0
This gives us two possible solutions for x:
x = 0 or x = 8
However, since the sides of a triangle cannot have a length of 0, the only valid solution is:
x = 8
Therefore, the sides of the right-angled triangle are 8cm, 15cm, and 17cm.