Question 255864: A house has two rooms of equal area. One room is square and the other room is a rectangle 4ft narrower and 5 ft longer than the square one. Find the area of each room
Answer by NRobinson(4)   (Show Source):
You can put this solution on YOUR website! The formula for Area is Area= Length * Width for both a rectangle or a square. The sides of a square are both equal. Let's call the length of each side of the square x. The measurements of the rectangle are listed as 4 feet narrower and the other side is 5 feet longer. This means their measurements are x-4 (the narrower side since narrower means smaller) and x+5 (since longer would be more).
The area of the square is x*x or x^2. The area of the rectangle is (x-4)*(x+5). These two areas are equal by the first sentence. So x^2=(x-4)(x+5). We use FOIL (first, outer, inner, last) to multiply out the right side.
x^2=x^2+5x-4x-20. Simplify terms of the same degree (same exponent value)
x^2=x^2+x-20.
Next we set the left side equal to zero by subtracting x^2 from both sides.
0=x-20
Now solve for x.
x=20.
Remember that x was the length of the sides of the square so our value has units of feet (from the second sentence).
The solution asks for the area of each room so we will need to determine this by going back to the area formula. Since the areas are equal we don't need to calculate both, but we can to double check our work (what's better then knowing you did everything right?!)
Area=length * width. The length and with of the square are both 20.
Area of the square= 20*20=400. Now don't forget units! The solution is 400 square feet (or ft^2)
Double check:
Area of the rectangle=Length* width. The two sides are (20-4)=16 and (20+5)=25 (remember x was 20) 16*25=400. We did everything correctly!!!
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