Question

Sides of a triangle are in ratio 13 : 14 : 15 and its perimeter is 84 cm. Find its area.

Answer 1

Answer :

Let the sides of the triangle be 13x, 14x and 15x respectively.

Perimeter = 13x+14+15x

=> 84 = 42x

=> x = 2

The sides of the triangle are :-

13x = 13*2 = 26 (a)

14x = 14*2 = 28 (b)

15x = 15*2 = 30 (c)

Semi - Perimeter (s) = Perimeter/2

=> semi - Perimeter (s) = 84/2

=> semi - Perimeter (s) = 42

$Area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c}$

$=> \sqrt{42(16)(14)(12)} = 336$

Area of triangle = 336 cm sq.

Hope this helps you ☺☺

Answer 2

$\huge\mathfrak{Answer}$

Here given that

Perimeter of a triangle = 84 cm

Sides are in the ratio 13 : 14 : 15

Total of ratio = 42 cm

$a = \frac{13}{42} \times 84 = 26cm$

$b = \frac{14}{42} \times 84 = 28cm$

$c = \frac{15}{42} \times 84 = 30cm$

$s = \frac{84}{2} = 42cm$

By Heron's Formula

$area = \sqrt{s(s - a)(s - b)(s - c)}$

$= \sqrt{42(42 - 26)(42 - 28)(42 - 30}$

$= \sqrt{42 \times 16 \times 14 \times 12} {cm}^{2}$

$= \sqrt{2 \times 3 \times 7 \times 4 \times 4 \times 2 \times 7 \times 3 \times 4} {cm}^{2}$

2 × 3 × 7 × 4 × 2 cm² = 336 cm²

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