SOLUTION: A house had two rooms of equal area. One room is square and the other roon is a rectangle 4ft narrower and 5ft longer than the square one. Find the area of each room.

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: A house had two rooms of equal area. One room is square and the other roon is a rectangle 4ft narrower and 5ft longer than the square one. Find the area of each room.      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 174169: A house had two rooms of equal area. One room is square and the other roon is a rectangle 4ft narrower and 5ft longer than the square one. Find the area of each room.
Found 2 solutions by jim_thompson5910, scott8148:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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%5E2=%28x%2B5%29%28x-4%29


x%5E2=%28x%2B5%29%28x-4%29 Start with the given equation.


x%5E2=x%5E2%2Bx-20 FOIL


0=x%5E2%2Bx-20-x%5E2 Subtract x%5E2 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%5E2=400 square feet.


So the length of the rectangle is 20%2B5=25 ft and the width is 20-4=16 ft. So the area of the rectangle is 25%2A16=400 square feet.

Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
areas are equal

let x=side of square room

x^2 = (x-4)(x+5)

x^2 = x^2 + x - 20

subtracting x^2-20 __ 20 = x

one room is 20x20 and the other is 16x25