Question

the sides of a triangle plot are in ratio of 3 ratio 5 ratio 7 and the perimeter is 300 M find the area

Answer 1

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Answer 2

☘️ Solution :

Suppose that the sides, in metres, are 3x, 5x and 7x.

Then, we know that 3x + 5x + 7x = 300 (perimeter of the triangle)

Therefore, 15x = 300, which gives x = 20.

So, the sides of the triangle are 3 × 20 m, 5 × 20 m and 7 × 20 m i.e., 60 m, 100 m, and 140 m.

Using Heron's formula :

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

So, now we have

$\sf \: s = \dfrac{60 + 100 + 140}{2} \: m = 150$

and area will be,

$\implies \sf \: \sqrt{150(150 - 60) \: (150 - 100) \: (150 - 140) }\: m^{2} \\ \\ \implies \sf \: \sqrt{150×90×50×10}~m^{2}\\ \\ \implies \sf \purple{1500 \sqrt{3} m^{2}}$

☘️ Answer :

• 1500√3^2