Question

The sides of a triangle are in the ratio 13:14:15and its perimeter is 84cm. Find the area of the triangle.

Answer 1

Let the sides be 13x, 14x and 15x
Perimeter = Sum of all sides
84 = 13x + 14x + 15x
42x = 84
x = 2
So, the sides are a = 26 cm, b = 28 cm and c = 30 cm
s = p/2 = 84/2 = 42 cm
Area = √s(s - a)(s - b)(s - c)
= √42(42 - 26)(42 - 28)(42 - 30)
= √42*16*14*12
= 4√14*14*36
= 4*14*6
= 336 cm^2
So, area of triangle = 336 cm^2

Answer 2

Let the sides of the triangle be 13x,14x and 15x.
Therefore, 13x+14x+15x=84
42x=84
x=2
Hence, sides of the triangle are 26 cm , 28 cm & 30 cm.
Area of the triangle =√s*(s-a)*(s-b)*(s-c). [Heron's Formula]
s=a+b+c/2=26+28+30/2= 84/2=42. a=26cm
Area=√42*(42-26)*(42-28)*(42-30). b=28 cm
Area=√42* 16*14*12. c=30 cm
Area=√42*2688
Area=√112896
Area=336 cm²