A Rectangular swimming pool has a length of 48 feet and width of 36 feet a hose needs to extend from the southwest corner of the pool to the north east corner of the pool. What is the shortest length the holes can be to extend from one corner to the another corner.
To find the shortest length the hose needs to be to extend from the southwest corner to the northeast corner of the pool, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the length and width of the pool form the legs of a right triangle, with the hose being the hypotenuse.
Using the Pythagorean theorem, we can calculate the length of the hose:
Length of the hose = √(Length^2 + Width^2)
Length of the hose = √(48^2 + 36^2)
Length of the hose = √(2304 + 1296)
Length of the hose = √3600
Length of the hose = 60 feet
Therefore, the shortest length the hose can be to extend from the southwest corner to the northeast corner of the pool is 60 feet.
To find the shortest length of the hose that extends from the southwest corner to the northeast corner of the rectangular swimming pool, you can use the Pythagorean theorem.
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the two sides of the right-angled triangle are the length and width of the pool, and the hypotenuse represents the length of the hose.
Let's label the sides of the right-angled triangle as follows:
- Length of the pool (base) = 48 feet
- Width of the pool (height) = 36 feet
- Length of the hose (hypotenuse) = ?
Applying the Pythagorean theorem:
Length of the hose squared = Length of the pool squared + Width of the pool squared
Length of the hose squared = 48^2 + 36^2
Length of the hose squared = 2304 + 1296
Length of the hose squared = 3600
To find the length of the hose, we take the square root of both sides:
Length of the hose = √3600
Length of the hose = 60 feet
Therefore, the shortest length the hose can be to extend from the southwest corner to the northeast corner of the pool is 60 feet.