The length of the sides of a triangle are in the ratio of 4:5:3
Answers
first we want to divide 180 from 12 and then with will the answer come multiply the answer with the 45 and 3 then + them all the answer will come
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Question :-
The length of the sides of a triangle are in the ratio of 4:5:3 and it's perimeter is 96 cm. Find it's area.
Solution :-
Let us consider of a triangle be 4x, 5x and 3x
Perimeter = Sum of sides = 4x + 5x + 3x
= 96 cm = 12x
x = 8
Now,
Sides of triangle = 4x = 4 × 8 = 32 cm
= 5x = 5 × 8 = 40 cm
= 3x = 3 × 8 = 24 cm
Apply, Heron's Formula
Area = √s(s-a) (s-b) (s-c)
= √48 × (48 × 32) (48 - 40) (48 - 24)
= √48 × 16 × 8 × 24
= √8 × 6 × 8 × 2 × 8 × 3
= √8⁴ × 36
= 64 × 6