Question

The Sides of a triangle are $24cm$, $18cm$ and $30cm$. Find:
$1.$ Area of triangle
$2.$ Height of the triangle corresponding to the smallest side.
$3.$ Height of the triangle corresponding to the longest side.

Answer 1

REF. Image.

Consider,

${18}^2+{24}^2$

$=324+576=900={30}^2$

i.e. ${18}^2+{24}^2={30}^2$

Hence the given triangle is a right-angled triangle.

Hence,

(a) Area of $△ABC=\frac{1}{2}\times 18\times 24c{m}^2=216c{m}^2$

(b) Since $AB\perp BC$, height corresponding to shortest side $AB$, is $BC=24cm$

(c) Let height required be $h$ we know, Area of $△=\frac{1}{2}\times base\times height$

$\Rightarrow ar\left(△ABC\right)\frac{1}{2}\times 30\times hc{m}^2$

$\Rightarrow 216c{m}^2=15hcm$

$\Rightarrow h=14.4cm$