Q. 15.0( 2 Votes )

The length of the sides of a triangle are in the ratio 4:5:3 and its perimeter is 96cm. Find it’s area.

Answer :

As the length of the side is in the ratio 4:5:3.


Let the sides be a, b and c whose lengths be 4k, 5k and 3k respectively. (Where k is some arbitrary constant).


Now Perimeter of triangle = 96 cm.


we get 4k + 5k + 3k = 96


12 k = 96


k = k = 8.


Sides become a = 4k = 4 × 8 = 32cm


b = 5k = 5 × 8 = 40cm


c = 3k = 3 × 8 = 24 cm


We get sides a, b, c as 32 cm, 40 cm and 24 cm respectively.


Now we need to find area of triangle with sides 32cm, 40cm and 24cm.


by Heron’s formula we get area of triangle


=


(where s = s is called as the semi perimeter )…(1)


we get


Substituting value of s, a, b and c in equation 1 we get



=


=


The area of triangle is 384cm2.


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