Question 174169
Let x=side length of square


Since "A house had two rooms of equal area. One room is square and the other room is a rectangle 4ft narrower and 5ft longer than the square one.", this means that {{{x^2=(x+5)(x-4)}}}



{{{x^2=(x+5)(x-4)}}} Start with the given equation.



{{{x^2=x^2+x-20}}} FOIL



{{{0=x^2+x-20-x^2}}} Subtract {{{x^2}}} from both sides.



{{{0=x-20}}} Combine like terms.



{{{20=x}}} Add 20 to both sides.




So the answer is {{{x=20}}} which means that the side length of the square is 20 ft. So the area of the square is {{{20^2=400}}} square feet.



So the length of the rectangle is {{{20+5=25}}} ft and the width is {{{20-4=16}}} ft. So the area of the rectangle is {{{25*16=400}}} square feet.