Question
The radius of a circle inscribed in any triangle whose sides are $a, b,$ and $c$ is given by the following equation, in which $s$ is an abbreviation for $(a+b+c) \div 2$ Check this formula for dimensional consistency.$$r=\sqrt{\frac{(s-a)(s-b)(s-c)}{s}}$$
Step 1
Step 1: First, we need to understand that the sides of the triangle $a, b, c$ and the radius $r$ of the inscribed circle are all lengths, and therefore have the same dimension, which we denote by $m$ (for meters). Show more…
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The radius of a circle inscribed in any triangle whose sides are $a, b,$ and $c$ is given by the following equation, in which s is an abbreviation for $(a+b+c) \div 2$. Check this formula for dimensional consistency. $$r=\sqrt{\frac{(s-a)(s-b)(s-c)}{s}}$$
The radius $r$ of a circle inscribed in any triangle whose sides are $a, b$, and $c$ is given by $$ r=[(s-a)(s-b)(s-c) / s]^{1 / 2} $$ where $s$ is an abbreviation for $(a+b+c) / 2 .$ Check this formula for dimensional consistency.
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