The length of the hypotenuse of the triangle is 2√985, when x = 8.
To find the length of the hypotenuse (c) of the right-angled triangle when x = 8, where the perpendicular side is 6x + 6 and the base is 4x, we can use the Pythagorean Theorem.
The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (perpendicular and base).
c^2 = (6x + 6)^2 + (4x)^2
Substitute x = 8 into the equation:
c^2 = (6(8) + 6)^2 + (4(8))^2
c^2 = (54)^2 + (32)^2
c^2 = 2916 + 1024
c^2 = 3940
Now, take the square root of both sides to find the length of the hypotenuse (c):
c = √3940
c = 2√985
Therefore, when x = 8, the length of the hypotenuse of the triangle is 2√985.