Question

Given isosceles triangle ABC with legs AB and BC, with AB = 4x - 3, BC = 3x + 5, and AC = 7x - 1, find AC.

a) AC = 4x - 3
b) AC = 3x + 5
c) AC = 7x - 1
d) AC = 4x + 2

Answer 1

To find the length of AC in an isosceles triangle, we can use the Pythagorean theorem and solve for x before finding AC.

Step-by-step explanation:

To find the length of AC, we need to use the fact that it is the hypotenuse of an isosceles triangle. By using the Pythagorean theorem, we can set up the equation (4x - 3)^2 + (3x + 5)^2 = (7x - 1)^2. Expanding and simplifying this equation will give us the value of x. Once we have x, we can substitute it into the expression for AC to find its length.

Answer: AC = 7x - 1.