Answer:
x = 12
Step-by-step explanation:
You know the triangle is a right triangle because the segment marked 16 is tangent to the circle. A tangent always makes a right angle with a radius.
The Pythagorean theorem works well for this. The sum of the squares of the legs of the right triangle is equal to the square of the hypotenuse.
x^2 + 16^2 = (x +8)^2
x^2 +256 = x^2 +16x + 64 . . . . simplify
16x = 192 . . . . subtract 64+x^2
x = 12 . . . . . . . divide by the coefficient of x
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You can also recognize that the difference in lengths of the shortest and longest sides of the triangle is half the length of the middle side. That means the ratios of the sides of this right triangle are 3:4:5, so x = (3/4)·16 = 12.
