Question

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

Answer 1

Step-by-step explanation:

3:4:5=144

3x + 4x + 5x = 144

12x = 144

X = 144/12

X = 12

1st side of triangle is 3×12 = 36

2nd side of triangle is 4×12= 48

3rd side of triangle is 5×12=60

then for finding area apply semiperimeter formula

36+48+60÷2 = 144/2

= 72

72(72-36)(72-48)(72-60)

= 864

the height corresponding to longest side

864= 1/2×60×height

864/30 = height

=28.8

The height corresponding to the longest side is 28.8 cm.

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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..