in the given figure, what is the value of x? the value of x is in. (round to the nearest tenth as needed.)

Answer

Explanation:

Step1: Apply Pythagorean theorem

Let the radius of the circle be (x). The right - triangle has legs (x) and (24) and hypotenuse (x + 16). According to the Pythagorean theorem (a^{2}+b^{2}=c^{2}), so (x^{2}+24^{2}=(x + 16)^{2}).

Step2: Expand the equation

Expand ((x + 16)^{2}) using the formula ((a + b)^{2}=a^{2}+2ab + b^{2}). We get (x^{2}+576=x^{2}+32x+256).

Step3: Simplify the equation

Subtract (x^{2}) from both sides of the equation: (576=32x + 256).

Step4: Solve for (x)

Subtract 256 from both sides: (32x=576 - 256=320). Then divide both sides by 32, (x = 10).