A right-angled triangle of has sides of length (3x-1)cm, x cm and (3x+1) cm. The value of x is *
since x is clearly [positive, the hypotenuse is 3x+1 (the longest side). So,
(3x-1)^2 + x^2 = (3x+1)^2
x = 12
So, now you know another handy Pythagorean triple: 12-35-37
To find the value of x in the right-angled triangle, we can use the Pythagorean theorem, which states that the sum of the squares of the lengths of the two shorter sides of a right-angled triangle is equal to the square of the length of the longest side (hypotenuse).
In this case, the two shorter sides are (3x-1) cm and x cm, and the longest side (hypotenuse) is (3x+1) cm.
Using the Pythagorean theorem, we have:
(3x-1)^2 + x^2 = (3x+1)^2
Expanding the squares:
9x^2 - 6x + 1 + x^2 = 9x^2 + 6x + 1
Simplifying the equation:
10x^2 - 12x = 0
Factoring out x:
x(10x - 12) = 0
Setting each factor equal to zero:
x = 0 or 10x - 12 = 0
If x = 0, we have a degenerate triangle with all sides equal to zero, which is not possible.
Solving 10x - 12 = 0 for x:
10x = 12
x = 12/10
x = 6/5
Therefore, the value of x is 6/5.
To find the value of x, we need to use the fact that the triangle is a right-angled triangle. In a right-angled triangle, the square of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides.
So, using the Pythagorean theorem, we can write the following equation:
(3x+1)^2 = (3x-1)^2 + x^2
Let's solve this equation step by step:
Expand the squares:
9x^2 + 6x + 1 = 9x^2 - 6x + 1 + x^2
Combine like terms:
9x^2 - 9x^2 + 6x - (-6x) + 1 - 1 = x^2
Simplify:
12x = x^2
Divide both sides by x:
12 = x
The value of x is 12.