Question

A triangle whose sides are $18cm$ $,24cm$ and $30cm$, has the length of altitude corresponding to the largest side of the triangle as $14.4cm$.
If true then enter $1$ and if false then enter $0$

Answer 1

Area of triangle with $a,b,c$ as sides and
$s=\frac{a+b+c}{2}$ is $\sqrt{s(s-a)(s-b)(s-c)}$.
For triangle with sides 18 cm, 24 cm and 30 cm, $s=\frac{18+24+30}{2}=36cm$
Area of the triangle with sides $18cm,24cm$ and $30cm=\sqrt{36(36-18)(36-24)(36-30)}$

$=\sqrt{36\times 18\times 12\times 6}$

$=\sqrt{18\times 2\times 18\times 6\times 2\times 6}$

$=18\times 6\times 2$

$=216{cm}^2$

Let the height for base $30cm$, be $h$
Area of triangle $=\frac{1}{2}\times \text{base}\times \text{height}=216c{m}^2$
$\Rightarrow \frac{1}{2}\times 30\times h=216$
$\Rightarrow h=14.4cm$