To find the length of the hypotenuse of a right triangle, we need to use the Pythagorean Theorem, which states that 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 (a and b):
c^2 = a^2 + b^2
In this case, we have two sides with lengths given by the expressions 5x + 7 and 3x. When x = 14, we can substitute this value into the expressions to find the lengths of the sides:
a = 5x + 7 = 5(14) + 7 = 77
b = 3x = 3(14) = 42
Now we can use the Pythagorean Theorem to find the length of the hypotenuse:
c^2 = a^2 + b^2 = 77^2 + 42^2 = 5929 + 1764 = 7693
Taking the square root of both sides, we get:
c = sqrt(7693) ≈ 87.7
Therefore, when x = 14, the length of the hypotenuse of the triangle is approximately 87.7 units. I