Question

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

Answer 1

Let the length of each side be 3x cm, 4x cm and 5x cm respectively
perimeter  = (3x +4x + 5x)
144 = 12x
   x = 12
Sides of triangle are 36cm, 48cm, 60cm respectively.
 let p = half of perimeter = 72
area = sqrt[p(p-a)(p-b)(p-c)] = sqrt[72*36*24*12] = sqrt[746496] = 864 cm^2

Answer 2

hi mate,

answer :The area of triangle is 864 cm² and the height corresponding to the longest side is 28.8 cm.

Step-by-step explanation:

The length of the sides of a triangle are in the ratio 3:4:5. Let the length of sides be 3x,4x,5x.

It is given that the perimeter of the triangle is 144 cm.

Let

the side = 3 x 4 x 5 x

144 = 3x + 4 x + 5 x

x = 144 / 12

x = 12

now we multiply by

3* 12 = 36 Cm = a

4* 12=48cm = b

5* 12=60cm = c = base....

S = a+b+c/2

36 + 48 + 60/2

144/2 = 72

triangle area = √ s (s - a) (s-b) ( s-c)

triangle area

= √ 72 (72-36) (72-48) (72-60)

triangle area = √72 (36) (24) (12)

triangle area = √746496

triangle area=864cm²

triangle area = ½ * base * height

864 = ½* 60 *height

864 = 30 *height

height = 864/30 = 28.8 cm

The height corresponding to the longest side is 28.8 cm.

i hope it helps you..