Question

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

Answer 1

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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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Answer 2

$\large\bf\underline{\underline{Given:-}}$

$\longmapsto$ The sides of a triangular plot are in the ratio of 3:5:7

$\longmapsto$ Its perimeter  is 300 m

$\large\bf\underline{\underline{To \ find:-}}$

$\longmapsto$ Its area

$\large\bf\underline{\underline{Answer:-}}$

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

So, let the sides of the triangle be 3x, 5x and 7x.

Also it is given that the perimeter of the triangle is 300 m therefore,

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

$\Longrightarrow$ 15x = 300

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

$\Longrightarrow\displaystyle\underline{x = 20}$

Therefore, the sides of the triangle are 60,100 and 140.

Now using herons formula:

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

$\displaystyle S = \frac{60 + 100 + 140}{2} = \frac{300}{2} = 150m$

Area of triangle:

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

$\displaystyle\Longrightarrow A = \sqrt{150(150 - 60)(150 - 100)(150 - 140)}$

$\displaystyle\Longrightarrow \sqrt{150\times 90\times 50\times 10}$

$\displaystyle\Longrightarrow \sqrt{6750000}$

$\displaystyle\Longrightarrow 1500 \sqrt{3}m^2$

Therefore, $\displaystyle \ area \ of \ triangle \ plot \ is \ 1500 \sqrt{3}m^2$

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