Final answer:
To find the length of AB, use the Pythagorean theorem and solve for x. Then substitute the value of x back into the equation to find the length of AB.
Step-by-step explanation:
To find the length of AB, we can use the concept of the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, AB is the hypotenuse of a right triangle with sides BC and AC. So, we can set up the equation:
AB^2 = BC^2 + AC^2
Substituting the given values:
(2x-3)^2 = (2x-3)^2 + (2x+10)^2
Expanding and simplifying the equation:
4x^2 - 12x + 9 = 4x^2 - 24x + 9 + 4x^2 + 40x + 100
Combining like terms:
-12x = -24x + 40x + 100 - 9
Simplifying the equation further:
-12x = 16x + 91
Bringing all the x terms to one side:
14x = -91
Dividing both sides by 14:
x = -91/14
Substituting the value of x back into AB:
AB = 2(-91/14) - 3
Simplifying the equation:
AB = -182/14 - 3
AB = -13.14 cm