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

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Question 173887: A house has two rooms of equal area. One room is square and the other room is a rectangle 4 ft narrower and 5 ft longer than the square room. Find the area of each room.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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: A house has two rooms of equal area. One room is square and the other room
is a rectangle 4 ft narrower and 5 ft longer than the square room.
Find the area of each room.
:
Let x = side of the square room
then
x^2 = area of the square room
:
(x+5) = length of the rectangular room
(x-4) = width of the rectangular room
Find the area of the rectangular room
A = (x+5)*(x-4) = area
FOIL
A = x^2 + x - 20
:
Rect area = square area
x^2 + x - 20 = x^2
:
x^2 - x^2 + x = +20
:
x = 20 ft side of the square (A = 400 sq/ft)
and
20+5 = 25 ft length of rect room
20-4 = 16 ft width of rect room (A = 400 sq/ft)