Question

⇒The sides of a triangular plot are in the ratio 3:5:7 and its perimeter is 300m. Find its area?

Answer 1

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Refer the attachment ✌

Answer 2

Given:-

• The sides of the triangular plot are in the ratio 3:5:7
• The perimeter is 3oo m.

To find:-

• Area of the triangular plot

Solution:-

Let the common multiple of the sides be 'a'

So the sides of the triangle are 3a, 5a and 7a.

Also, We know that the perimeter of the triangle is 300 m.

The formula for perimeter of triangle is:-

P = Side1 + side2 + side3

So,

⇴ 300 = 3a + 5a + 7a

⇴ 300 = 15a

⇴ a = $\frac{300}{15}$

⇴ a = 20

So, the first side is 3a

⇴ 3 × 20

⇴ 60

The second side is 5a

⇴ 5 × 20

⇴ 100

The third side is 7a

⇴ 7 × 20

⇴ 140

Now, by herons formula:-

⇴ S = $\frac{60+100+140}{2}$

⇴ S = $\frac{300}{2}$

⇴S = 150 m

Area of triangle is

⇴ A = $\sqrt{s(s-a)(s-b)(s-c)}$

⇴ A = $\sqrt{150(150-60)(150-100)(150-140)}$

⇴ A = $\sqrt{150×90×50×10}$

⇴ A = $\sqrt{6750000}$

⇴ A = 150 $\sqrt{3}$ m²

Thus the area of the triangle is 150 $\sqrt{3}$ m²