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? Check all that apply.

y(y + 5) = 750
y2 – 5y = 750
750 – y(y – 5) = 0
y(y – 5) + 750 = 0
(y + 25)(y – 30) = 0

Answer 1

Hello,

A:False
B:True
C:True
D:False
E:True

Answer 2

Option B , C and E are correct

`y^2-5y =750`

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

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

Explanation:

Given : Area of rectangular room is 750 square feet.

Width of the room is 5 feet less than the length of the room.

Let y be the length of the room

then,

As per the given condition

width of the room is: y-5

Area of rectangle is multiply the length by its width.

Area of rectangle =
`length * width`

Substitute the given values in above formula we get;

`750 = y(y-5)` ......[1]

or we can write this as;

750 -y(y-5)=0

[1] ⇒
`y(y-5) =750` or

`y^2-5y =750` or

`y^2-5y-750=0`

`y^2-25y+30y-750=0`

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

Therefore, the equation which can be used to solve for y are;

`y^2-5y =750` ,
`750 -y(y-5)=0` and (y+25)(y-30)=0