Question

Find the unknown side length, x. Write your answer in simplest radical form

Answer 1

Answer choice C

Explanation:

By the Pythagorean Theorem, the square of the length of the hypotenuse is equal to the sum of the squares of the legs. You can rearrange this to find one of the legs using the other two sides of the right triangle:

`x=√(24^2-10^2)=√(576-100)=√(476)=√(2^2\cdot 119)=2√(119)`

Therefore, the correct answer is choice C. Hope this helps!

Answer 2

C. 2√119

Explanation:

To do this you can use the Pythagorean theorem where a^2 + b^2 = c^2. a and b represent the legs and c represent the hypotenuse. We can rearrange the equation and get c^2-b^2=a^2, and substitue 24 for c and 10 for b. This means 24^2-10^2=a^2. This simplifies to 576-100=a^2, or 476=a^2.

This means that √476=a, but we can simplify this as √4*119 and turn that into 2√119, or C. As 119 cannot be divided by any more perfect squares, this is the simplest form.