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.

A rectangle is shown. Diagonals are drawn from each point to the opposite point and intersect in the middle. The top left point is push-ups, the top right point is Jump rope, the bottom left point is lunges, the bottom right point is sit-ups, and the middle point is free weights. The distance from push-ups to lunges is 3 feet. The distance from sit-ups to free weights is 2.5 feet.

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?

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devilchild0351 devilchild0351 · Answer 1 · 2020-04-15T01:32:47+02:00

Answer:

2.5ft

3ft

4ft

5ft

Step-by-step explanation:

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boffeemadrid boffeemadrid · Answer 2 · 2021-11-13T10:46:13+01:00

The distances of each station is required.

2.5 feet

3 feet

4 feet

5 feet

The distance between pushups and lunges is 3 feet.

The distance between free weights and sit-ups is 2.5 feet

[tex]PL=3\ \text{feet}[/tex]

[tex]FS=2.5\ \text{feet}[/tex]

In a rectangle the diagonals are equal and bisect each other so

[tex]FS=PF=2.5\ \text{feet}[/tex]

The opposite side of PL which is JS = 3 feet because it is a rectangle.

The distance between push up station and Jump rope is

[tex]JS^2+PJ^2=PS^2\\\Rightarrow PJ=\sqrt{PS^2-JS^2}\\\Rightarrow PJ=\sqrt{5^2-3^2}=4\ \text{feet}[/tex]

Since, the diagonals are equal [tex]PS=JL[/tex]

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