A park is in the shape of an isosceles triangle and its base and altitude are  in theratio of 3:2. If the cost of levelling the park at the rate of Rs 18.50 per meter square is Rs 88800 find the sides of the park

Asked by tejvarun | 10th Jan, 2016, 03:19: PM

Expert Answer:

Given, 
Base : Altitude = 3 : 2
Cost of levelling park = Rs.88800
Rate per mete square = Rs.18.50
 
So, Area of the park = fraction numerator 88800 over denominator 18.5 end fraction = 4800 m2
Let the common multiple be x.
Then, Base = 3x and Altitude = 2x
 
Area of a triangle = 1 half cross times b cross times h
4800 = 1 half cross times 3 x cross times 2 x
4800 = 3x2
x2 = 4800 ÷ 3
x2 = 1600
x2 = 40 × 40
x = 40
 
Base = 3 × 40 = 120 m
Height = 2 × 40 = 80 m
 
In an isosceles triangle, the altitude divides the base in to two equal parts. Altitude is  perpendicular to the base. 
According to Pythagoras theorem, 
(hypotenuse)2 = (side 1)2 + (side 2)2
= (80)2 + (120 ÷ 2)2

= (80)2 + (60)2
= 6400 + 3600 
= 10000
Hypotenuse = 100 m 
 
So, both isosceles sides of the park are 100 m respectively. 
 
Hence, the length of the sides of the park are 100 m, 100m and 120m respectively. 
 
 

Answered by Keravi Thanani | 11th Jan, 2016, 11:12: AM

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