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.
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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