Question

solve for x. round to the nearest tenth if necessary.
a. 3
b. 6.3
c. 12.8
d. 40

Explanation:

Step1: Use area formula

$\frac{1}{2}\times5\times8=\frac{1}{2}\times x\times8$

Step2: Solve for x

$x = \frac{5\times8}{8}=5$ (but this is wrong, correct is using geometric - mean theorem).
Let the two - segment lengths on the hypotenuse be $a = 5$ and the other part be $b$. The altitude is $h = 8$.
We know that $h^{2}=a\times b$, so $b=\frac{64}{5}$. Then $x=a + b=5+\frac{64}{5}=\frac{25 + 64}{5}=\frac{89}{5}=12.8$

Answer:

C. 12.8