Question

The sides of a triangular plot are in ratio of 3:5:7 and is perimeter is 300m find its area

Answer 1

let the sides be =x
ATQ
3x+5x+7x=300
15x=300
x=300/15
x=20m
sides
3(20)=60
5(20)=100
7(20)=140

s=300/2=150

area by herons formula
√S-(s-a)(s-b)(s-c)

√150(150-60)(150-100)(150-140)

√150(90)(50)(10)

√2x5x3x5x2x5x3x3x2x5x5x2x5

2x2x3x5x5x5√3


1500√3 m^2. ans

Answer 2

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

Assumption

Sides be 3p , 5p and 7p

Hence

3p + 5p + 7p = 300 (Perimeter of ∆)

8p + 7p = 300

15p = 300

$\tt{\rightarrow p=\dfrac{300}{15}}$

p = 20

Therefore

${\boxed{\sf\:{Sides\;are:-}}}$

3p = 3 × 20 = 60

5p = 5 × 20 = 100

7p = 7 × 20 = 140

${\boxed{\sf\:{Assume}}}$

a = 60m

b = 100m

c = 140m

$\tt{\rightarrow s=\dfrac{a+b+c}{2}}$

$\tt{\rightarrow s=\dfrac{60+100+140}{2}}$

$\tt{\rightarrow s=\dfrac{300}{2}}$

s = 150 m

Now,

${\boxed{\sf\:{Using\;Herons\;Formula}}}$

$\tt{\rightarrow\sqrt{s(s-a)(s-b)(s-c)}}$

$\tt{\rightarrow\sqrt{150(150-60)(150-100)(150-140)}}$

$\tt{\rightarrow\sqrt{150\times 90\times 50\times 10}}$

$\tt{\rightarrow 1500\sqrt{3}m^2}$