Question

The perimeter of a triangle is 300m. If its sides are in the ratio 3:5:7 find its area by using herons formula ??

Answer 1

Let triangle ABC
AB= 3x   ; BC= 5x   ; AC= 7x
  Perimeter= 300m
AB+BC+AC= 300
3x+5x+7x= 300
15x= 300
x= 300/15= 20

∵AB= 3x= 3(20)= 60m
  BC= 5x= 5(20)= 100m
  AC= 7x= 7(20)= 140m

             S= a+b+c/2= 300/2= 150
 Area= √s(s-a)(s-b)(s-c)
            √150(150-60)(150-100)(150-140)
            √150*90*50*10
            √2*3*5*5*2*3*3*5*2*5*5*2*5
            2*2*3*5*5*5*√3
            1500√3 m² 

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 :

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

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