6. The lengths of the sides of a triangle are in the ratio of 3:4:5 and its
perimeter is 14cm. Find the area of the triangle?
tell the steps also
pls help
Answers
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.
3x+4x+5x=1443x+4x+5x=144
12x=14412x=144
x=12x=12
The value of x is 12. It means the length of sides are 36,48,60.
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.
or you can learn from this image
