Question

The lengths of sides of a triangle are in the ratio $3:4:5$ and its perimeter is $144$ cm, then find the height corresponding to largest side.

• A. $14.8$ cm
• B. $28.8$ cm
• C. $39$ cm
• D. $16$ cm

Answer 1

The correct option is

A

$28.8$ cm

Given, Side of triangle are in ratio $3:4:5$ and their perimeter $144cm$

Let the sides of triangle be $3x,4x,5x$

Perimeter $3x+4x+5x=$ 144 cm

$12x=144$

$\therefore x=12$

Then sides of triangle are $3x$$=$ 3$\times$12$=$ 36 cm,

$4x$$=$ 4$\times$12$=$ 48 cm,

$5x$$=$ 5$\times$12$=$ 60 cm.

Now,Semi perimeter, $s=\frac{Sumofsidesoftriangle}{2}$

$=\frac{36+48+60}{2}=72cm$

Using heron's formula, Area of triangle$=\sqrt{s(s-a)(s-b)(s-c)}$

$=\sqrt{72(72-36)(72-48)(72-60)}$

$=\sqrt{72\times 36\times 24\times 12}=864{cm}^2$
Using altitude, area of triangle$=\frac{1}{2}\times$ base $\times$ altitude $=864{cm}^2$

$=\frac{1}{2}\times 60\times$ altitude $=864$

$\therefore$ altitude $=\frac{864\times 2}{60}=28.8cm$

So, altitude corresponding to largest side is 28.8 cm.