Answer: the length of one side of the bedroom is 24 feet.
the length of one side of the closet is 3 feet
Explanation:
Let x represent the length of one side of the bedroom.
Let y represent the length of one side of the closet.
The sides of the bedroom were 8
times as large as the sides of the closet. This means that
x = 8y
the sum of the areas of the two was
585 square feet. The area of the room is x^2 and the area of the closet is y^2. Therefore,
x^2 + y^2 = 585 - - - -- - - -1
Substituting x = 8y into equation 1, it becomes
(8y)^2 + y^2 = 585
64y^2 + y^2 = 585
65y^2 = 585
y^2 = 585/65 = 9
Take square root of both sides of the equation,
y = √9 = 3
x = 8y = 8×3 = 24