Question

the lengths of the sides of a triangle are in the ratio 2:3:4 and it's perimeter is 144 CM. Find (i) the area of the triangle and (ii) the height corresponding to the longest side. give the answer with the explanation​

Answer 1

Answer :-

The area of triangle is 743.6128025cm² and the height corresponding to the longest side is 23.23790008cm.

Step-by-step explanation:-

The length of the sides of a triangle are in the ratio 2:3:4. Let the length of sides be 2x,3x,4x,

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

Let,

sides are 2x, 3x, 4x

perimeter = 2x + 3x + 4 x

144 = 2x + 3x + 4 x

x = 144 / 9

x = 16

now we substitude the value of x

2×16 = 32m = a

3×16= 48cm = b

4×16= 64 cm = c = base....

S = ( a+b+c)/2

(32 + 48 + 64 )/2

144/2 = 72

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

triangle area

= √ 72 (72-32) (72-48) (72-64)

triangle area = √72 (40) (24) (8)

triangle area = √552960

triangle area=743.6128025cm²

Triangle area = ½ × base × height

743.6128025= ½ × 64 × height

743.6128025 = 32× height

height = 743.6128025/32

= 23.23790008 cm

The height corresponding to the longest side is 23.23790008cm.

i hope it helps you..