Question

the length of the sides of a triangle are in the ratio of 3:4:5 and its perimeter is 144 cm. find the height corresponding to the longest side.

Answer 1

Let side a = 3x
Let side b =4x
Let side c =5x
Perimeter of triangle = AB+BC+CA
144 cm = 3x+4x+5x
144 cm = 12x
x = 144/12
x = 12 cm
Side a = 3x
= 3*12
= 36 cm
Side b = 4x
= 4*12
= 48 cm
Side c = 5x
=5*12
= 60 cm

Answer 2

Let the sides of the triangle be 3x cm, 4x cm and 5x cm.

Perimeter of the triangle = 144 cm

∴ 3x + 4x + 5x = 144

⇒ x = 12

So, the sides of the triangle are 36 cm, 48 cm and 60 cm.

Semi perimeter of triangle, s = 72 cm

Area of triangle =
$\sqrt{s(s - a) \: (s - b) \: (s - c) }$
=
$\sqrt{72 \times 36 \times 24 \times 12 \:} \: cm {}^{2}$
=
$864 \: cm {}^{2}$
Longest side = 60 cm

Also, area of triangle = 
$\frac{1}{2} \times b \times h$
⇒ 864 = 
$\frac{1}{2} \times 60 \times b$
⇒ h = 28.8 cm

So, the height corresponding to longest side is 28.8 cm.