Question

2. The sides of a triangular plot are in the ratio 3:5:7 and its perimeter is 300 m. Find its area.
Take root 3 = 1.732.​

Answer 1

Given :

• The sides of a triangular plot are in the ratio 3:5:7.
• Perimeter of triangular plot is 300 m.

To find :

• Area of triangular plot?

Solution :

☯ Let sides of triangle be 3x, 5x and 7x.

We know that,

Perimeter of Triangle = Sum of all its sides

Here,

• Perimeter of triangular plot is 300 m.

⇒ 3x + 5x + 7x = 300

⇒ 15x = 300

⇒ x = 300/15

⇒ x = 20

Therefore,

• 3x = 3 × 20 = 60 m
• 5x = 5 × 20 = 100 m
• 7x = 7 × 20 = 140 m

∴ Sides of triangular plot is 60 m, 100 m and 140 m.

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☯ Now, Using Heron's Formula,

⇒ s = semi - perimeter

⇒ s = 60 + 100 + 140/2

⇒ s = 300/2

⇒ s = 150 m

☯ Now, Area of triangle is,

⇒ A = √(s - a)(s - b)(s - c)

⇒ A = √150(150 - 60)(150 - 100)(150 - 140)

⇒ A = √150 × 90 × 50 × 10

⇒ A = √6750000

⇒ A = 1500√3 m² or 2598 m²

∴ Hence, Area of triangular plot is 1500√3 m² or 2598 m².

Answer 2

Step-by-step explanation:

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$\text{\large\underline{\red{Given:-}}}$

Sides of a triangular plot are in the ratio 3:5:7.

Perimeter of the plot is 300m.

$\text{\large\underline{\purple{To find}}}$

Area of the triangular plot.

$\text{\large\underline{\pink{Solution:-}}}$

Firstly we will find the sides of triangular plot :

$\longmapsto\tt\bold{Let\:sides\:be=3x,5x\:and\:7x}$

$\longmapsto\tt{3x+5x+7x=300}$

$\longmapsto\tt{15x=300}$

$\longmapsto\tt{x=\cancel\dfrac{300}{15}}$

$\longmapsto\tt\bold{x=20}$

So , The sides of Triangular plot are 60m , 100m and 140m.

Now ,

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

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

$\longmapsto\tt{\cancel\dfrac{300}{2}}$

$\longmapsto\tt\bold{150m.}$

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

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

$\longmapsto\tt{\sqrt{150\times{(90)}\times{(50)}\times{(10)}}}$

$\longmapsto\tt{\sqrt{3\times{5}\times{5}\times{2}\times{3}\times{3}\times{5}\times{2}\times{5}\times{2}\times{5}\times{5}\times{2}}}$

$\longmapsto\tt{3\times{5}\times{5}\times{5}\times{2}\times{2}\sqrt{3}}$

$\longmapsto\tt\bold{1500\sqrt{3}{m}^{2}}$

Therefore , The Area of the Triangular Plot is 1500√3m²...

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