Question

The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0

Answer 1

Answer:

$750 - y(y-5)=0$

Step-by-step explanation:

Data: Area of the room = 750 square feet

         Width = Lenght - 5 feet

We have a rectangular room. To calculate it's area we do:

Area = Width x Length

We know that width depends on Lenght in this exercise. Replacing our data above:

750 square feet = (Length - 5 feet) x Lenght

Let's rearrange our equation. If we named Lenght = y :

$750 = y (y-5)$

Now we do one more final step to match one of the options:

$750 - y(y-5)=0$

If you look carefully, there are two more correct answers similar to the equation above:

$y^{2}-5y=750$

Answer 2

Answer:

$y^{2}-5y=750$

$750-y(y-5)=0$

$(y + 25)(y -30) = 0$

Step-by-step explanation:

Givens

• The area of a rectangular room is 750 square feet.
• The width of the room is 5 feet less than the length of the room.

Let's call $w$ the width and $l$ the length. According to the problem they are related as follows

$w=l-5$, because the width is 5 feet less than the lenght.

We know that the area of the room is defined as

$A=w\times l$

Where $A=750 ft^{2}$

Replacing the given area and the expression, we have

$750=(l-5)l\\750=l^{2}-5l \\l^{2}-5l-750=0$

We need to find two number which product is 750 and which difference is 5, those numbers are 30 and 25.

$l^{2}-5l-750=(l-30)(l+25)$

Using the zero property, we have

$l=30\\l=-25$

Where only the positive number makes sense to the problem because a negative length doesn't make any sense.

Therefore, the length of the room is 30 feet.

Also, the right answers are the second choice where $y=l$, the third choice and the last choice.