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.
