Question

The lengths of the sides of a triangle are in the ratio $3:4:5$ and its perimeter is $288cm$. The height of the triangle corresponding to the longest side is

• A. $14.4cm$
• B. $57.6cm$
• C. $28.8cm$
• D. $Noneofthese$

Answer 1

The correct option is A $14.4cm$

Lengths of the sides of a triangle are in ratio $3:4:5$

Lets say the sides are $3k,4k,5k$

Given that its perimeter is $288$cm

$\therefore 3k+4k+5k=28812k=288$

$k=24$cm

$\therefore$ The sides are of length $72$cm, $96$cm, $120$cm.

which form a pythagorean triplet.Hence we have a right angled triangle.

we need to find $BD$

Consider $△ABC$ & $△BDC$

$△ABC\sim △BDC$ by $AA$ criterion

$\angle ABC=\angle BDC$ (same angle)

sides are in proportion

$\Rightarrow \frac{shorterlegin△ABC}{shorterlegin△BDC}=\frac{hypotenusein△ABC}{hypotenusein△BDC}\Rightarrow \frac{72}{BD}=\frac{120}{96}\Rightarrow BD=57.6cm$