Question

the perimeter of a triangular field is 144m and ratio 3:4:5 . find its area through herons formula ?​

Answer 1

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Given

• Perimeter of triangle = 144m

• Ratio of sides = 3 : 4 : 5

To Calculate

• Area of Triangle by Heron's Formula

Solution

Let the sides be 3x, 4x and 5x

Perimeter of △ = 144m

3x + 4x + 5x = 144

12x = 144

x = 144/ 12

x = 12

Sides of triangle

• 3x = 3 × 12 = 36m
• 4x = 4 × 12 = 48m
• 5x = 5 × 12 = 60m

Now semi perimeter of △ is

$\bf= \frac{36 + 48 + 60}{2}$

$\bf = \frac{144}{2}$

$\bf = 72$

a = 36m, b = 48m and c = 60m

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

$\bf \implies\sqrt{72(72 - 36)(72 - 48)(72 - 60)}$

$\bf \implies\sqrt{72 \times 36 \times 24 \times 12}$

$\bf\implies\sqrt{746496}$

$\bf \implies864 {cm}^{2}$

Therefore, Area of triangle is 864 sq.cm.

Answer 2

Given

• Perimeter of triangle = 144m

• Ratio of sides = 3 : 4 : 5

To Calculate

• Area of Triangle by Heron's Formula

Solution

Let the sides be 3x, 4x and 5x

$\bf \implies Perimeter \: of △ = 144m$

$\bf \implies 3x + 4x + 5x = 144$

$\bf \implies 12x = 144$

$\bf \implies x = 144/ 12$

$\bf \implies x = 12$

Sides of triangle

• 3x = 3 × 12 = 36m

• 4x = 4 × 12 = 48m

• 5x = 5 × 12 = 60m

Now semi perimeter of △ is

$\bf Semi \: Perimeter \: of △ = \frac{144}{2}$

$\bf Semi \: Perimeter \: of △ =72$

a = 36m, b = 48m and c = 60m

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

$\bf \implies\sqrt{72(72 - 36)(72 - 48)(72 - 60)}$

$\bf \implies\sqrt{72 \times 36 \times 24 \times 12}$

$\bf\implies\sqrt{746496}$

$\bf \implies864 {cm}^{2}$

Therefore, Area of triangle is 864 sq.cm.