Question

The perimeter of a triangular plot is 600 m. If the sides are in the ratio 5:12:13, the
find the area of the plot.​

Answer 1

$\sf{\underline{\boxed{\large{\blue{\mathsf{Solution}}}}}}$

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

• Perimeter = 600
• Sides = 5 : 12 : 13

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$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

• Area = ???

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$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

$\sf{\red{\boxed{\bold{perimeter = a + b + c }}}}$

• Let each side be 5x , 12x , 13x

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: $\sf\implies\:{\bold{ 600 = 5x + 12x + 13x }}$

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: $\sf\implies\:{\bold{ 30x = 600 }}$

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: $\sf\implies\:{\bold{ x = \dfrac{600}{30}}}$

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: $\sf\implies\:{\bold{ x = 20 }}$

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• Finding each side

5x = 5 x 20 = 100m

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12x = 12 x 20 = 240m

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13x = 13 x 20 = 260m

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$\sf{\red{\boxed{\bold{Semi\: Perimeter = \dfrac{ a + b + c }{ 2 }}}}}$

$\sf{\red{\boxed{\bold{area = \sqrt{ s ( s - a ) ( s - b ) ( s - c )}}}}}$

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• Finding semi perimeter

: $\sf\implies\: {\bold{ s = \dfrac{ 100 + 240 + 260 }{2}}}$

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: $\sf\implies\: {\bold{ s = \dfrac{ 600 }{2}}}$

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: $\sf\implies\: {\bold{ s = 300 m}}$

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• Finding area

: $\sf\implies\: {\bold{ area = \sqrt{ 300 ( 300 - 100 ) ( 300 - 240) ( 300 - 260 )}}}$

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: $\sf\implies\: {\bold{ area = \sqrt{ 300\times 200 \times 60 \times 40}}}$

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: $\sf\implies\: {\bold{ area = \sqrt{ 3\times 10 \times 10 \times 2 \times 10 \times 10 \times 2 \times 3 \times 10 \times 10 \times 2 \times 2 }}}$

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: $\sf\implies\: {\bold{ area = 2 \times 3 \times 2 \times 10 \times 10 \times 10}}$

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: $\sf\implies\: {\bold{ area = 12000 m^2}}$

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$\sf{\pink{\boxed{\bold{area = 12000 m^2}}}}$

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$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

• Area of triangle = $\sf{\bold{ 12000m^2 }}$

Answer 2

Answer :

Let x be each side.

5x + 12x + 13x = 600

30x = 600

x = 600/30

x = 20

5x = 100

12x = 240

13x = 260

Area of triangle = bh/2

= 100*240/2

= 24000/2

= 12000m².