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:
[tex]A=width*length[/tex]
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:
[tex]Y=X-5[/tex]
Now, using the area equation we have:
A=width*length
[tex]750=X*Y[/tex] but using the width expression we have:
[tex]750=X*(X-5)[/tex]
[tex]0=X^2-5X-750[/tex]
Using the root's equation we have:
[tex]X=\frac{-b\±\sqrt{b^{2}-4ac}}{2a}[/tex]
[tex]X=\frac{-(-5)\±\sqrt{(-5)^{2}-(4*1*(-750)}}{2*1}[/tex]
[tex]X1=30[/tex]
[tex]X1=-25[/tex]
Because the length (X) can't be negative, then length=30 feet. In order to find the width we have:
[tex]Y=X-5[/tex]
[tex]Y=30-5[/tex]
[tex]Y=25[/tex]
So the width is 25 feet.
In conclusion the room has a width=25 ft and length=30 ft.
