Question

the cost of fencing a triangular plot with sides in the ratio 5:12:13 is rupees 25. if the total cost is rupees 2250,then are of the plot is ?
The answer is 270m^2 . can someone please tell the method ?​

Answer 1

Hey Buddy

Here's The Answer

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Given :

• fencing cost Rs 25 per meter
• sides ratio 5 : 12 : 13
• Total cost of fencing Rs. 2250

To find :

• Area ( A )

Formula used :

• Area ( A ) = √ [ S( S - a ) ( S - b ) ( S - c ) ] Herons formula.

Solution :

Let the side be 5x, 12x, 13x, as they are in ratio

=> Perimeter = 5x + 12x + 13x

=> Perimeter = 30x meters

Now cost for fencing 30x meter at the rate of Rs. 25 per meter.

=> Cost = 25 × 30x

=> Cost = Rs. 750x

Given cost is Rs. 2250.

=> 750x = 2250

=> x = 2250/750

=> x = 3

So the actual sides are

• 5x => 5 × 3 = 15 meters
• 12x => 12 × 3 = 36 meters
• 13x => 13 × 3 = 39 meters

• Let, a = 15m, b = 36m and c = 39m

Now finding the area using herons formula.

S = ( sum of all sides )/2

=> S = ( 15 + 36 + 39 )/2

=> S = 90/2

=> S = 45

Area ( A ) = √ [ S( S - a ) ( S - b ) ( S - c ) ]

=> A = √ [ 45 ( 45 - 15 ) ( 45 - 36 ) ( 45 - 39 ) ]

=> A = √ [ 45 ( 30 ) ( 9 ) ( 6 ) ]

=> A = √ 72900

=> A = 270 m²

Area of triangular field is 270 m².

Hope It Helps.

Answer 2

$\sf{ \bold{ \underline{ \green{answer \: to \: the \: question}{} }{} }{} }{}$

»Question :-

• the cost of fencing a triangular plot with sides in the ratio 5:12:13 is rupees 25. if the total cost is rupees 2250,then are of the plot is ?

The answer is 270?

»Answer

$\sf{ \bold{ \red{given \: from \: the \: question}{} }{} }{}$

• Fencing cost = ₹25 per meter

• Side ratio = 5:12:13

• Total cost of fencing = ₹2250

$\sf{ \bold{ \blue{to \: find \: out \: }{} }{} }{}$

• Area of the Triangular plot =?

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

• 5x, 12x, 13x as they are the side ratios given

• perimeter of the triangular plot = Add all sides = 5x+12x+13x = 30x

• Now cost of fencing = ₹25 per meter

• So, cost = 25*30x = 750x.

Given the total cost of fencing = ₹2250

• 750x = 2250

• x = 2250/750 = 3

So, the actual sides = 5x = 15 ,12x = 36, 13x= 39

Let a = 15,b = 36 and c = 39

• semiperimeter (s) = Half of perimeter

• perimeter = 15+36+39= 90

• So, the semiperimeter = 90/2 = 45meters

Now area = root of [s(s-a)(s-b)(s-c)]

• [45(45-15)(45-36)(45-39)

• [45(40*9*6)]
• =>root of 72900

• There fore the area = 270 sq m

$\sf{ \bold{ \red{final \: answer \: = 270 \: sq \: m}{} }{} }{}$

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