Question

ALGEBRA 1, SEM. 2; please show work!

A rectangular flower bed is enlarged so that its area increases by 14 m². The enlarged flower bed is a rectangle and its area is x^2+9x+14 m².

Which expressions represent the dimensions of the flower bed before the increase?

*I ALREADY KNOW THE ANSWER IS X & X+9, I NEED TO KNOW WHY*

Answer 1

The enlarged flower bed is a rectangle and its area is x^2+9x+14 m²

So before its enlargement by 14 m², the area of the rectangle = x^2+9x

As you know, the area of rectangle is equal length times width

so area = x^2+9x

factors:

x^2+9x = x (x + 9)

So the dimensions are x and (x + 9)

Hope it helps.