The lengths of the sides of a triangle are in the ratio 3:4:5 and its perimeter is 144cm. Find the area of the triangle and the height corresponding to the longest side
Answers
Step-by-step explanation:
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=2a+b+c
s=\frac{144}{2}=72s=2144=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=21×base×height
864=\frac{1}{2}\times 60 \times height864=21×60×height
height=\frac{864}{30}=28.8height=30864=28.8
The height corresponding to the longest side is 28.8 cm.