Rahul has a rectangular farm with a length of 26 m and a breadth of 18 m. He wants to build a
rectangular swimming pool inside the farm which is at a distance of x m from all the sides of the farm.
Find the algebraic expression for the base area of the swimming pool. If depth of the swimming pool
is x + 10 m, what is the expression for the amount of water that the pool can hold?
Answers
Solution :
Rahul has a rectangular farm with a length of 26 m and a breadth of 18 m.
Area of the farm :
> Length × Breath
> 26 × 18
> 468 m² .
The area of the swimming pool can't exceed the area of the farm .
So , the maximum possible area of the pool comes out to be 468 m² when x is negligible .
He wants to build a rectangular swimming pool inside the farm which is at a distance of x m from all the sides of the farm.
So, let's take the length .
Original length = 26m .
x m is subtracted from both sides
New Length = ( 26 - 2x )
New Breath = ( 18 - 2x )
> [ 26 - 2x ][ 18 + 2x ] is the area of the swimming pool .
For [ 26 - 2x ][ 18 + 2x ] ≤ 468, we can obtain the optimal value of x ; although it isn't mentioned here .
Volume of pool :
> [ 26 - 2x ][ 18 + 2x ] [ x + 10 ] m³.
1 m³ = 1 liter.
Thus , the capacity of the pool becomes [ 26 - 2x ][ 18 + 2x ] [ x + 10 ] liters .
This is the required answer .
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