Need help please

[Reccless]

A house has two rooms of equal area. One room is square and the other is rectangle four feet narrower and five feet loger than the square one. Find the area of each room. Any info would be very helpful.

 

[Daniel_Feldman]

Area=length x width, right?

So let A=lw represent the area of either the square or the rectangle. I'll use the square to solve this.

Area of square=lw

Area of rectangle=(l+5)(w-4)=lw-4l+5w-20

Now, two more pieces of information you need to use to solve it:

The areas are equal, so lw-4l+5w-20=lw

Thus 5w-4l-20=0

Also, remember that all sides of a square are equal, so l=w. Thus, the equation can be re-written as

5l-4l-20=0

l=20

l=w, so

w=20


Area of the square room (dimensions 20 X 20)=400ft^2

Area of rectangular room (dimensions 25 X 16)=400ft^2

 

[Denis]

Let x = sides of square; then rectangle = (x - 4) by (x + 5)

x^2 = (x - 4)(x + 5)
x^2 = x^2 + x - 20
x = 20 ; rectangle = 16 by 25