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? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0

Answer 1

1) y² - 5y = 750

2) 750 -y(y -5) = 0

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

Explanation:

Area of rectangle = 750 ft²

length = y ft

width = (y - 5) ft

Area of rectangle = 750

length * width = 750

y (y -5) = 750

• Expand the equation,

y*y - 5*y = 750

y² - 5y = 750

• y(y - 5 )= 750

0 = 750 - y(y -5)

750 - y(y-5) = 0

• y² - 5y = 750

y² - 5y - 750 = 0

Sum = -5

Product = -750

Factors = -30 , 25 {-30 + 25 = -5 & (-30)*25 = -750}

y² - 30y + 25y - 750 = 0 {Rewrite the middle term using the factors}

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

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