If the sides of a triangle are in the ratio 8:4:5 and its perimeter is 72 cm, find the area
of the triangle.
Answers
As given in the question
Sides of the triangle are in ratio 8:4:5
Let the sides be 8x cm, 4x cm and 5x cm.
Also given
perimeter of the triangle is 72 cm
We know
Perimeter of the triangle is the sum of the sides of triangle i.e. Sum of length of three sides = perimeter
or
(8x + 4x + 5x) cm = 72 cm
17x = 72
or
x = 72/17
Thus sides of triangle are 8(72/17), 4(72/17) and 5(72/17)
= 576/17, 288/17 and 360/17 cm respectively
Also perimeter = 72
s (semi perimeter) = 36
Using Heron's formula
Area of triangle =
Now
s= 36
s-a = 36 - (576/17) = (612-576)/17 = 36/17
Similarly
s-b = (612-288)/17 = 324/17
and s-c = (612-360)/17 = 252/17
Using the following values in Heron's formula
By solving
Also 324 is square of 18
Area =
Thus area is approximately equal to 146.7 cm^2
P.s. - Unique set of sides, may be there is an error in the question itself.
Nevertheless,
Same method will be used for such type of questions.