The length of side of triangle are in the ratio 3: 4: 5 and its perimeter is 144 centimetre find (1)the area of triangle and (2) the height corresponding to the longest side
Answers
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.
3x+4x+5x=144
12x=144
X=144÷12
X=12
3x=3×12=36
4x=4×12=48
5x=5×12=60
so, length of the three sides are 36,48,60.
Using heron's formula the area of triangle is
A=√s(s-a)(s-b)(s-c)
Where,
s=a+b+c/2
s=144/2
s=72
The area of triangle is
A=√72(72-36)(72-48)(72-60)=846
The area of triangle is 864 cm².
The area of triangle is 1/2×base×height
864=1/2×60×h
h=864/30=28.8
The height corresponding to the longest side is 28.8 cm.
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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..