Question

The side of a triangular plot are in the ratio of 3:5:7 and it's perimeter is 300. find its area
​

Answer 1

Answer:

3x+5x+7x=300

15x=300

so,X=300/15=20

now,

3x=3*20=60

5x=5*20=100

7x=7*20=140

Answer 2

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

Ratio is 3 : 5 : 7

Assume

Sides are

3p , 5p and 7p

Hence,

Perimeter of Triangle = 300m

Then,

3p + 5p + 7p = 300

15p = 300

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

p = 20

Therefore,

3p = 3 × 20 = 60m

5p = 5 × 20 = 100m

7p = 7 × 20 = 140m

Now,

Semi Perimeter of Triangle

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

Area of ∆

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

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

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

$\tt{\rightarrow \sqrt{3\times 50\times 3\times 30\times 50\times 10}}$

$\tt{\rightarrow \sqrt{3\times 3\times 50\times 50\times 10\times 10\times 3}}$

$\tt{\rightarrow 3\times 50\times 10\sqrt{3}}$

→ Area = 1500√3 m²

Therefore ,

Area of ∆ is 1500√3 m²