Incorrect Answer For Mini-Question?

[Aaron Wang]

For the mini question, shouldn't the answer be

$$r={\sqrt{(s-a)(s-b)(s-c)}\over s}$$

instead of

$$r={\sqrt{(s-a)(s-b)(s-c)\over s}}$$

The denominator shouldn't be inside the square root, right?

[debbie]

@aaron-wang Thanks for asking! Actually, the area formula equals $\sqrt{ s(s-a)(s-b)(s-c)},$ which I can write like this: $\sqrt{s}\sqrt{(s-a)(s-b)(s-c)}.$ So since the area of the triangle is equal to $rs,$ dividing this by $s$ makes the $\sqrt{s}$ cancel out but leaves a $\sqrt{s}$ on the bottom.

$$\begin{aligned} r &= \frac{\textcolor{red}{\sqrt{s}} \sqrt{(s-a)(s-b)(s-c)}}{\textcolor{red}{s}} \\\\ &= \frac{\textcolor{red}{\sqrt{s}} \sqrt{(s-a)(s-b)(s-c)}}{\textcolor{red}{\sqrt{s}\sqrt{s}}} \\\\ &= \frac{\sqrt{(s-a)(s-b)(s-c)} }{\sqrt{s}}\\ \end{aligned}$$

[Aaron Wang]

@debbie Ah, ok! So since the denominator is

$$\sqrt{s}$$

it gets combined into that bigger square root.

[Aaron Wang]

This post is deleted!

[debbie]

@aaron-wang

You got it!