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. which equations can be used to solve for y, the length of the room?

Answer 1

I hope this helps you

Answer 2

Answer:

Width=25 ft and length=30 ft

Step-by-step explanation:

In order to find the answer let's remember that the area (A) of a rectangle is:

$A=width*length$

Let's assume that the length of the room is 'X' feet.

Becuase the problem mentioned that the width (Y) of the room is 5 feet less than the length, then:

$Y=X-5$

Now, using the area equation we have:

A=width*length

$750=X*Y$ but using the width expression we have:

$750=X*(X-5)$

$0=X^2-5X-750$

Using the root's equation we have:

$X=\frac{-b\±\sqrt{b^{2}-4ac}}{2a}$

$X=\frac{-(-5)\±\sqrt{(-5)^{2}-(4*1*(-750)}}{2*1}$

$X1=30$

$X1=-25$

Because the length (X) can't be negative, then length=30 feet. In order to find the width we have:

$Y=X-5$

$Y=30-5$

$Y=25$

So the width is 25 feet.

In conclusion the room has a width=25 ft and length=30 ft.