Question

the length of the sides of a triangle are in the ratio 3:4:5and it's perimeterr is 144 find the area if the triangle ​

Answer 1

side 1=3x

side 2=4x

side 3 =5x

3x+4x+5x=144

12x=144

x=144/12

x=12

s 1=3×12=36

s 2=4×12=48

s 3=5×12=60

36+48+60=144

Answer 2

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..