Question

Area of a triangle is 216 cm² abd its sides are in the ratio of 3:4:5. find the perimeter of the triangle

Answer 1

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Area of the triangle = 216 cm²

Let the ratio of sides of triangle be 3x,4x and 5x

From the first two sides we get,

$\frac{3x \times 4x}{2} = 216 \\ \\ = > \frac{3x \times 4x }{432} \\ \\ = > 12 {x}^{2} = 432 \\ \\ = > {x}^{2} = \frac{432}{12} \\ \\ = > {x}^{2} = 36 \\ \\ = > x = 6$

Thus, the sides of the triangle are

3x = 3×6 = 18

4x = 4×6 = 24

5x = 5×6 = 30

Now,

Perimeter = 18+24+30

= 72

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Answer 2

The ratio of the sides of the triangle = 3 : 4 : 5
=> 3x, 4x, 5x

The area of the triangle = 216 cm

So, take first 2 sides.

3x*4x / 2 = 216
=> 3x*4x / 432
=> 12x^2 = 432
=> x^2 = 432/12
=> x^2 = 36
=> x = 6 

Then find the sides of the triangles = 3(6) + 4(6) + 5(6)
=> 18 + 24 + 30
=> 72 cm