Question

Can you please solve this fast because my session keeps timing out

Answer 1

The Solution:

The given figure is

We are required to find the value of x in the given figure above.

Step 1:

We shall find an expression for m by considering the right-angled triangle ABD.

By the Pythagorean Theorem,

$m^2=x^2+16^2\ldots eqn(1)$

Similarly, considering the right-angled triangle ACD, we can find an expression for n.

By the Pythagorean Theorem,

$n^2=x^2+4^2\ldots eqn(2)$

Now, in the right-angled triangle ABC, we have by the Pythagorean Theorem that:

$20^2=m^2+n^2\ldots eqn(3)$

Putting eqn(1) and eqn(2) into eqn(3), we get

$\begin{gathered} 20^2=x^2+16^2+x^2+4^2 \\ 400=2x^2+16^2+4^2 \end{gathered}$$\begin{gathered} 400=2x^2+256+16 \\ 400=2x^2+272 \\ \text{collecting the like terms, we get} \\ 400-272=2x^2 \end{gathered}$$\begin{gathered} 2x^2=128 \\ \text{Dividing both sides by 2, we get} \\ \frac{2x^2}{2}=\frac{128}{2} \\ \\ x^2=64 \end{gathered}$

Taking the squared root of both sides, we get

$\begin{gathered} \sqrt[]{x^2}=\sqrt[]{64} \\ \\ x=\pm8 \\ \text{That is,} \\ x=8\text{ or x=-8} \\ \text{ We shall discard -8 since a length cannot be negative. } \\ \text{ So, the value of x is 8. That is, x=8} \end{gathered}$

Therefore, the correct answer is 8.