ICSE Class 8 Answered
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 | 10 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 = 
= 4800 m2
= 4800 m2Let the common multiple be x.
Then, Base = 3x and Altitude = 2x
Area of a triangle = 
4800 = 
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 | 11 Jan, 2016, 11:12: AM
