Question

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

Answer 1

Question

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

$\rule{300}{1}$

Answer

Let's consider the side of the plot as 3x, 5x and 7x.

So the sum of all these sides would be 300 m.

Now we need to do this equation to find the value of 'x' ⇒ $3x+5x+7x=300$

Let's solve your equation step-by-step

$3x+5x+7x=300$

Step 1: Simplify both sides of the equation.

$3x+5x+7x=300$

(Combine Like Terms)

$(3x+5x+7x)=300$

$15x=300$

Step 2: Divide both sides by 15.

$\frac{15x}{15} =\frac{300}{15}$

$x= 20$

Now the sides of the triangle would be ⇒

Side A ⇒ 3×20 = 60 m

Side B ⇒ 5×20 = 100 m

Side C ⇒ 7×20 = 140 m

According to Heron Law we find area with this formula ⇒ $\sqrt{s(s-a)(s-b)(s-c)}$

Over here 's' is the half of the perimeter which is 300 here. So the value of p would be 150.

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

$\sqrt{150(90)(50)(10)}$

$\sqrt{150(45000)}$

$\sqrt{6750000}$

$1500\sqrt{3}m^{3}$

∴ The area would be 1500√3m³.

$\rule{300}{1}$

Answer 2

Answer:

$\blue{{\textbf{\underline{\underline{According\:to\:the\:Question}}}} }</p><p>$

Ratio is 3 : 5 : 7

Assume

Sides are

3p , 5p and 7p

Hence,

Perimeter of Triangle = 300m

Then,

3p + 5p + 7p = 300

15p = 300

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

p = 20

Therefore,

3p = 3 × 20 = 60m

5p = 5 × 20 = 100m

7p = 7 × 20 = 140m

Now,

Semi Perimeter of Triangle

$\orange{\tt{\dfrac{60+100+140}{2}}}</p><p>$

Area of ∆

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

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

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

$</p><p>\tt{ \sqrt{3\times 50\times 3\times 30\times 50\times 10}}</p><p></p><p></p><p></p><p>$

$\pink{\tt{ \sqrt{3\times 3\times 50\times 50\times 10\times 10\times 3}}}</p><p></p><p>$

${\tt{ 3\times 50\times 10\sqrt{3}}}</p><p>$

→ Area = 1500√3 m²

Therefore ,

Area of ∆ is 1500√3 m²