Arectangle swimming pool is 4 ft deep. one side of the pool is 2.5 times longer than the other. the amount of water needed to fill the swimming pool is 1960 cubic feet. find the dimensions of the pool. (find largest and smallest)

The dimensions of the pool are length is 35 feet and width is 14 feet.

Given that,

A rectangle swimming pool is 4 ft deep.

One side of the pool is 2.5 times longer than the other.

The amount of water needed to fill the swimming pool is 1960 cubic feet.

We have to determine,

Find the dimensions of the pool. (find largest and smallest).

According to the question,

The area of the pool by dividing the volume by the depth:

The pool is 490 square feet.

And The area is found by multiplying the length by the width.

Let, The width of the pool is X.

One side of the pool is 2.5 times longer than the other.

Length is 2.5X (2.5 times longer)

Then,

The width of the pool is 14 feet,

And The length is = 2x = 2.5 (14) = 35 feet.

Hence, The required dimensions of the pool are length is 35 feet and width is 14 feet.

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Find the are of the pool by dividing the volume by the depth:

1960 / 4 = 490

The pool is 490 square feet.

Area is found by multiplying the length by the width.

Let the width = X

We are told the length is 2.5X ( 2.5 times longer)

So we now have 2.5x * x = 490

2.5x * x = 2.5x^2

Now we have 2.5x^2 = 490

Divide both sides by 2.5:

x^2 = 490/2.5

x^2 = 196

find X by taking the square root of 196:

x = √196

x = 14

The width is 14 feet

The length is 2.5 * 14 = 35 feet