The perimeter of a triangle whose
sides are in the ratio 3:4:5 is 24 cm.
What is the area of this triangle?
Answers
Answer:
28.8
Step-by-step explanation:
Given, Side of triangle are in ratio 3:4:5 and their perimeter 144 cm
Let the sides of triangle be 3x,4x,5x
Perimeter 3x+4x+5x= 144 cm
12x=144
∴x=12
Then sides of triangle are 3x= 3×12= 36 cm,
4x= 4×12= 48 cm,
5x= 5×12= 60 cm.
Now,Semi perimeter, s=2Sumofsidesoftriangle
=236+48+60=72cm
Using heron's formula, Area of triangle=s(s−a)(s−b)(s−c)
=72(72−36)(72−48)(72−60)
=72×36×24×12=864cm2
Using altitude, area of triangle=21× base × altitude =864cm2
=21×60× altitude =864
∴ altitude =60864×2=
Answer:
Step-by-step explanation:
Let the ratios be x
First side = 3x and the other two sides are 4x and 5x respectively
now , perimeter of triangle is the sum of the sides
therefore , 3x + 4x + 5x = 24cm (given perimeter)
12x = 24 cm
x = 2 cm
therefore
first side = 6 cm
2nd side = 8 cm
3rd side = 10 cm
Now , Area of triangle by heron's formula =
√ [s (s – a) (s – b) (s – c)]
S = 24 cm /2 = 12 cm
Therefore , Area =
√[ 12(12-6)(12-8)(12-10)]
√[12 x 6 x 4 x 2]
√[576] = 24cm^2