The figure shows two right triangles drawn at to each other. If , , and , find x and then find h . Round each answer to the nearest whole number.
A)
C)
D)

Question

The figure shows two right triangles drawn at   to each other.  ​ If  ,  , and  , find x and then find h . Round each answer to the nearest whole number. ​
A)​ 
C)​ 
D)​

Quizplus · Accepted Answer

Using the Pythagorean theorem, we have:

$10^2 + (2x)^2 = (x+10)^2$
$100 + 4x^2 = x^2 + 20x + 100$
$3x^2 - 20x = 0$
$x(3x-20) = 0$

Since $x$ cannot be zero, we have $3x-20=0$ which gives us $x=\frac{20}{3}$.

To find $h$, we can use the smaller right triangle:

$\frac{h}{10} = \frac{2x}{x}$
$h = 20$

Rounding to the nearest whole number, we get $x=7$ and $h=20$, so the answer is B.

The Figure Shows Two Right Triangles Drawn at To