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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

Verified Answer :

caylus

Hello,

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

Answer:

Option B , C  and E are correct

\(y^2-5y =750\)

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

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

Step-by-step 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 = \(length \times width\)

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




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