Question

the cost of fencing a triangular plot with sides in the ratio 5:12:13 is rupees 40 per meter the cost incurred is 6000 what is the total area

Answer 1

Answer:

150m² - If you want to write in notebook copy the bold text

Step-by-step explanation:

As the ratio is 5:12:13, we can understand that the triangle is a right angled triangle (Pythagoras triplet).

(In Notebook you need to draw a triangle ABC with <B=90 and write -

Let's check whether the triangle is a right angled triangle or not -

If ∆ABC is right angled triangle, then

AC²= AB²+BC²

13x²= 12x²+5x²

169x²= 144x²+25x²

169x²=169x²

LHS=RHS

Hence, ∆ABC is a right angled triangle

The cost of fencing is Rs. 6000 at the rate of 40 m.

Cost of fencing= Rate of fencing(per m) * Perimeter

Perimeter = Cost of Fencing/ Rate of fencing

Perimeter = 6000/40

13x+5x+12x = 150

30x = 150

x=5

The sides of the triangle are 1. 13x = 13*5 = 65m

2. 12x = 12*5 = 60m

3. 5x = 5*5 = 25m

Area of the triangle = 1/2*b*h

=1/2*60*5

=30*5

=150m²

Answer 2

Given : the cost of fencing a triangular plot with sides in the ratio 5:12:13 is rupees 40 per meter the cost incurred is 6000

To Find :  the total area

Solution:

Side  5x , 12x  and 13x  

Perimeter = 5x + 12x + 13x  = 30x

Cost = 30x * 40  = 1200x

1200x = 6000

=> x = 5

5x , 12x  and 13x  

(13x)² = (5x)² + (12x)²

Hence using converse of Pythagorean theorem

this is a right angle triangle with base and height 5x and 12

Area = (1/2) 5x * 12x  = 30x²

= 30(5)²

= 750  m²

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