Question

The cost of painting a triangular piece of decoration wall, at the rate of * 27 per sq m is 81000. If
the sides of the plot are in the ratio 13:12:5, find its sides.
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Answer 1

Step-by-step explanation:

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Answer 2

The sides of triangle are 130 m, 120 m, 50 m

Given:

The cost of painting a triangular piece of decoration wall,

at the rate of Rs 27 per sq m is 81000 Rs.

The ratio the sides of the plot is 13:12:5

To find:

The sides of the plot

Solution:

Given Cost for decorating wall = 81000 Rs

And rate of cost = 27 Rs. per sq m

Then the area of the triangle = total cost / cost per sq m  

= 81000 Rs / 27 Rs. per sq m = 3000 sq m

Area of the triangle =  3000 sq m

Given the ratio of side = 13:12:5

Let 13x, 12, 5x are be the sides of triangle

As we know the formula for Area of triangle is given by

                 Area = √s(s-a)(s-b)(s-c)

Where s = semiperimeter and a, b and c are sides of triangle

Semiperimeter of the given triangle = (13x+12x+5x)/ 2 = 30x/2 = 15x

Area of the triangle = √15x(15x - 13x)(15x - 12x)(15x - 5x)  

= √15x(2x)(3x)(10x)  

= √900x⁴  

=  30x²  

We know the area of the triangle = 3000 sq m

⇒ 30x² = 3000

⇒  x² = 100

⇒   x = 10

Therefore, sides of triangle are

= 13x,  12x,  5x

= 13(10), 12(10), 5(10)

= 130, 120, 50

The sides of triangle are 130 m, 120 m, 50 m

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