Question

100 36 Find the value of x. Leave your answer in simplest radical form. Type your answer...

Answer 1

We will solve as follows:

We have that 100 is to sqrt(x^2+64^2) what 64 is to x, that is:

$\frac{100}{\sqrt[]{x^2+64^2}}=\frac{64}{x}$

Now, we solve for x:

$100x=64\cdot\sqrt[]{x^2+64^2}$

And simplifying, we will get:

$10000x^2=4096(x^2+4096)\Rightarrow10000x^2=4096x^2+4096^2$

Now, we operate like terms:

$10000x^2-4096x^2=4096^2\Rightarrow x^2(10000-4096)=4096^2$$\Rightarrow x^2(5904)=4096^2\Rightarrow x^2=\frac{4096^2}{5904}\Rightarrow x=\frac{1024}{3\sqrt[]{41}}$