THE SIDE OF A RIGHT-ANGLED TRIANGLE ARE 3XCM,3X-1CM AND 4X PLUS 1CM ,THE LAST SIDE BEING THE HYPOTHENUS FIND X.
solve:
(3x)^2 + (3x-1)^2 = (4x+1)^2
To find the value of x in the right-angled triangle with side lengths 3x cm, 3x-1 cm, and 4x + 1 cm, where the hypotenuse is 4x + 1 cm, we can use the Pythagorean theorem.
According to the Pythagorean theorem, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, we have:
(4x + 1)^2 = (3x)^2 + (3x - 1)^2
Expanding the equation:
16x^2 + 8x + 1 = 9x^2 + 9x^2 - 6x + 1
Combining like terms:
16x^2 + 8x + 1 = 18x^2 - 6x + 1
Subtracting (18x^2 - 6x + 1) from both sides:
16x^2 + 8x + 1 - 18x^2 + 6x - 1 = 0
-2x^2 + 14x = 0
Factoring out the common factor of -2x:
-2x(x - 7) = 0
Setting each factor equal to zero and solving for x:
-2x = 0 gives x = 0
x - 7 = 0 gives x = 7
Therefore, there are two possible values for x: x = 0 and x = 7.
However, since we are dealing with lengths in this problem, x cannot be zero. Therefore, the value of x in this right-angled triangle is x = 7.