Question

The perimeter of a triangle is 144 cm and the lengths of the sides are in the ratios 3:4:5. Find its area

Answer 1

Given, the length of sides of the triangle is the ratio 3 : 4 : 5.

and perimeter = 144cm

⇒ 3x + 4x + 5x =144

⇒ 12x =144

⇒ x =12cm

∴ shortest side = 3x = 3 ×12 = 36cm

side of medium length = 4x = 4 × 12 = 48cm

longest side = 5x = 5 ×12 = 60cm

Again s = semi-perimeter of Δ =144/2= 72cm

Using, heron's formula, area of Δ

figure

Equating (1) and (2), we get

30h=864
=h=28.8

Hence, the height of triangle corresponding to longest side is 28.8 cm.

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..