Question

The sides of triangle plot are in ratio 3:5:7. And its perimeter is 300m. Find its area.

Answer 1

Let the sides be 3x, 5x and 7x

perimeter of a ∆= Sum of all its sides

3x+5x+7x=300

15x=300

x=300/15

x=20

Sides,

3x=3×20

60

5x=5×20

100

7x=7×20

140

For area refer the above given image.

Answer 2

GiveN :-

• Sides of triangle are in ratio of 3:5:7

• Perimeter of triangle is 150 m

To FinD :-

• Area of the triangle

SolutioN :-

Let, Sides of triangle be 3x, 5x and 7x

$\longrightarrow \boxed{ \bf Perimeter \: of \: triangle = a + b + c } \\ \\\sf \longrightarrow3x + 5x + 7x = 300 \\ \\\sf \longrightarrow15x = 300 \\ \\\sf \longrightarrow x = \frac{300}{15} \\ \\ \sf \longrightarrow x = 20$

So, Sides are :

• 3x = 3×20 = 60 m

• 5x = 5×20 = 100 m

• 7x = 7×20 = 140 m

Now, Semi-perimeter of the triangle :

$:\implies \boxed{\bf s = \frac{a + b + c}{2} }\\ \\:\implies\sf s = \frac{60+100+140}{2} \\ \\:\implies\sf s = \frac{300}{2} \\ \\:\implies\sf s = 150$

Area of the triangle :

$:\implies\boxed{\bf Area = \sqrt{s(s - a)(s - b)(s - c)}} \\ \\:\implies\sf \sqrt{150(150- 60)(150- 100)(150 - 140 )} \\ \\:\implies\sf \sqrt{150 \times 90 \times 50 \times 10} \\ \\:\implies\sf \sqrt{50\times3 \times 5 \times2 \times 3 \times 3 \times 50 \times \times 5 \times2 } \\ \\:\implies\sf 50 \times 3 \times 5 \times 2 \times \sqrt{3} \\ \\:\implies\sf 1500 \sqrt{3} \: {m}^{2}$

$\large \therefore \underline{ \bf \blue{Area \: of \: triangle \: is \: {1500} \sqrt{3} \: {m}^{2}}}$