The sides of a triangle are $11m,60m$ and $61m.$ The altitude to the smallest side is

The correct option is A: $11m$

The area of a triangle (denoted by $A$) having sides $a,b,c$ and $s$ as semi-perimeter is given by

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

$s=\frac{a+b+c}{2}=\frac{11+60+61}{2}=\frac{132}{7}=66cm$

We need to find the altitude to the smallest side

$A=\sqrt{66(66-11)(66-60)(66-61)}$

$\Rightarrow A=\sqrt{66\times 55\times 6\times 5}$

$\Rightarrow A=\sqrt{108900}$

$\Rightarrow A=330m^2$

The area of a triangle having base $AC$ and height $P$ is given by

Area $\left(A\right)$ $=\frac{1}{2}$ $\times$ (Base $\times$ Height)

Area $\left(A\right)$ $=\frac{1}{2}\times (AC\times P)$

We need to find the height $P.$ Here the smaller side is $11m$.

$AC=11m$

$\Rightarrow 330=\frac{1}{2}\times (11\times p)$

$\Rightarrow 330\times 2=11\times p$

$\Rightarrow 660=11\times p$

$\Rightarrow p=\frac{660}{11}$

$\therefore p=60m$.

So, the altitude to the smallest side is $60m.$