the lengths of the sides of a triangle are in ratio 3:4:5find the area of triangle if it's perimeter is 144cm
Answers
Step-by-step explanation:
Perimeter :- 144 cm
Length Ratio - 3:4:5
let length be 3x:4x:5x
Perimeter of Triangle - Sum of its all three sides
According to Question ,
3x+4x+5x= 144
12x=144
x= 144/12
x = 12
3x = 3×12 = 36
4x = 4×12 = 42
5x = 5×12 = 60
Using heron's formula the area of triangle is
A=\sqrt{s(s-a)(s-b)(s-c)}A=
s(s−a)(s−b)(s−c)
Where,
s=\frac{a+b+c}{2}s=
2
a+b+c
s=\frac{144}{2}=72s=
2
144
=72
The area of triangle is
A=\sqrt{72(72-36)(72-48)(72-60)}=864A=
72(72−36)(72−48)(72−60)
=864
The area of triangle is 864 cm².
The area of triangle is
A=\frac{1}{2}\times base \times heightA=
2
1
×base×height
864=\frac{1}{2}\times 60 \times height864=
2
1
×60×height
height=\frac{864}{30}=28.8height=
30
864
=28.8
The height corresponding to the longest side is 28.8 cm.
Answer:
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