Answer: The area of a rectangular room is 750 square feet and the width of the room is 5 feet less than the length of the room.
Three equations that can be used to solve for y, the length of the room are:
y(y + 5) = 750: This equation uses the formula for the area of a rectangle, which is length x width. Since the width is 5 feet less than the length, we can substitute y-5 for the width.
750 – y(y – 5) = 0: This equation uses the same method as the first equation, but it is rearranged to solve for y.
(y + 25)(y – 30) = 0: This equation uses the quadratic formula to solve for the length of the room, this equation is also useful when the length is an irrational number.
Note that the fourth equation y(y – 5) + 750 = 0 is not valid because it is not possible to have negative area, hence y(y-5) should not be added to 750.
The fifth equation (y+25)(y-30)=0 is also not valid because it gives y = -25 and y = 30 as solutions but the length of the room can't be negative.
Explanation: