the lengths of a triangle are in ratio 3:4:5 and its perimeter is 144cm. find the area of the triangle and the highest corresponding to the longest side
please urgent
Answers
let the side 3x, 4x and 5x be Perimeter of the triangle = sum of all sides
144 = 3x + 4x +5x
144 = 12x
x = 12 cm
1st side be 3 * 12 = 36 cm
2nd side be 4 * 12 = 48cm
3rd side be 5 * 12 = 60 cm
formula = √ s (- a) (s-b) ( s-c)
s = 36 + 48 + 60/2
= 89
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..