Question

a fitness club wants to set up stations for four different workouts around the shelves of free - weights in the middle of the room. the trainer wants the distance from the free weights to each station to be the same, so he uses a rectangular shape, as shown in the diagram. push - ups 3 ft free weights 2.5 ft lunges sit - ups jump rope what is the distance from the free weights to the push - up station? what is the distance from the jump - rope station to the sit - up station? what is the distance from the push - up station to the jump - rope station? what is the distance from the lunge station to the jump - rope station? 2.5 ft 3 ft 4 ft 5 ft

Explanation:

Step1: Recall property of rectangle

In a rectangle, the diagonals bisect each other and are equal. The distance from the free - weights (center of rectangle) to each station is half of the diagonal length.

Step2: Use Pythagorean theorem

Let the length of the rectangle be $l = 4$ ft and width be $w = 3$ ft. The diagonal $d$ of a rectangle with length $l$ and width $w$ is given by $d=\sqrt{l^{2}+w^{2}}$. Here, $l = 4$ ft and $w = 3$ ft, so $d=\sqrt{4^{2}+3^{2}}=\sqrt{16 + 9}=\sqrt{25}=5$ ft. The distance from the free - weights to each station is $\frac{d}{2}=2.5$ ft.

Step3: Analyze side - lengths of rectangle

The distance between adjacent stations (e.g., jump - rope to sit - up, push - up to jump - rope) is either the length or the width of the rectangle. The length of the rectangle is 4 ft and the width is 3 ft.

1. The distance from the free weights to the push - up station: 2.5 ft
2. The distance from the jump - rope station to the sit - up station: 4 ft
3. The distance from the push - up station to the jump - rope station: 3 ft
4. The distance from the lunge station to the jump - rope station: 4 ft

Answer:

1. 2.5 ft
2. 4 ft
3. 3 ft
4. 4 ft