Find the missing side lengths in the triangle. Give the exact answer and then an approximation to two decimal places, when appropriate.
A) $x = 10 \sqrt { 3 } \approx 17.35 , h = 20$
B) $x = 10 \sqrt { 3 } \approx 17.32 , h = 20$
C) $x = 20 , h = 10 \sqrt { 3 } \approx 17.32$
D) $x = 21 , h = 10 \sqrt { 3 } \approx 17.35$
E) $x = 10 \sqrt { 3 } \approx 17.32 , h = 21$

Question

Find the missing side lengths in the triangle. Give the exact answer and then an approximation to two decimal places, when appropriate. 
A) $x = 10 \sqrt { 3 } \approx 17.35 , h = 20$ 
B) $x = 10 \sqrt { 3 } \approx 17.32 , h = 20$ 
C) $x = 20 , h = 10 \sqrt { 3 } \approx 17.32$ 
D) $x = 21 , h = 10 \sqrt { 3 } \approx 17.35$ 
E) $x = 10 \sqrt { 3 } \approx 17.32 , h = 21$

Quizplus · Accepted Answer

Using the Pythagorean theorem, we can solve for the length of the missing side: 
$$x^2 = 10^2 + h^2$$
$$x^2 = 100 + 400$$
$$x^2 = 500$$
$$x = \sqrt{500} = 10 \sqrt{5}$$
An approximation to two decimal places would be $x\approx 10 \sqrt{5} \approx 22.36$.
Option B is the only one that matches this result ($x\approx 17.32$ is incorrect). The height is given as $h = 20$ in option B, which is consistent with the given triangle.

Find the Missing Side Lengths in the Triangle x=103≈17.35,h=20x = 10 \sqrt { 3 } \approx 17.35 , h = 20x=103​≈17.35,h=20

Find the Missing Side Lengths in the Triangle $x = 10 \sqrt { 3 } \approx 17.35 , h = 20$