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# ICSE Class 8 Answered

<div>A park is in the shape of an isosceles triangle and its base and altitude are &nbsp;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</div>
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
Let 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