Question

What is the radius of the circle inscribed in a triangle having side lengths $35$ cm, $44$ cm and $75$ cm

• A. $3$ cm
• B. $4$ cm
• C. $5$ cm
• D. $6$ cm

Answer 1

The correct option is D $6$ cm

Area of the triangle $ABC$
$=\sqrt{s(s-a)(s-b)(s-c)}$,
where $s=\frac{1}{2}(a+b+c)$ and $AB=35,BC=75,CA=44$
Therefore, $△ABC=\sqrt{77\times (77-75)(77-44)(77-35)}c{m}^2$
$=\sqrt{77\times 2\times 33\times 42}c{m}^2$
$=\sqrt{7\times 11\times 2\times 3\times 11\times 2\times 3\times 7}$
$=(7\times 11\times 2\times 3)=462$
We have $△ABC=△BOP+△COA+△AOB$
Thus $463=\frac{1}{2}r(75+44+35)\Rightarrow r=6$ cm

Therefore, radius of the circle is $6$ cm.