the length of a side of triangle are in the ratio 3 is to 4 is to 5 and perimeter is 144 find the area of a triangle
Answers
3x + 4x + 5x = 144
12x = 144
x = 144/12 = 12
3x = 3 * 12 = 36
4x = 4 * 12 = 48
5x = 5 * 12 = 60
s = 144/2 = 72
By heron's formula,
Area of a triangle = √[s(s-a)(s-b)(s-c)]
= √ [72(72-36)(72-48)(72-60)]
= √ [ 72 * 36 * 24 * 12]
= 6 √ [ 12 * 6 * 4 * 6 * 12]
= 6 * 12 * 6 * 2
= 864 cm²
(: Hope this helpz :)
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..