Final answer:
To find the area of Lily's bedroom, you need to know the area of her square kitchen. By setting up the equation (1/4)y² = 1/4(yx)², you can determine that the side length of the kitchen is equal to the length of its width. Substituting the values, the area of Lily's bedroom is 144 square inches.
Step-by-step explanation:
The area of Lily's bedroom is 1/4 the area of her square kitchen.
To find the area of Lily's bedroom, we need to know the area of her square kitchen.
The problem states that the kitchen has x number of tiles going across each wall and each tile is 12 inches wide.
So, the side length of the kitchen can be found by multiplying x by 12 inches.
Let's assume the side length of the kitchen is y inches. Since the area of Lily's bedroom is 1/4 the area of her kitchen, we can set up the equation: (1/4)y² = 1/4(yx)². Simplifying this equation, we get y² = (yx)².
Next, we can solve for y.
Taking the square root of both sides, we have y = yx.
Dividing both sides by x, we get y = y.
Therefore, the side length of the kitchen (y) is equal to the length of its width (y).
Now, we can find the area of Lily's bedroom by using the formula A = (1/4)(y)², where A is the area.
Substituting y for x and solving the equation, we get A = (1/4)(y)²
= (1/4)(yx)²
= (1/4)(yx)(yx)
= (1/4)x²y².
Finally, substituting x and y with their respective values, we get A = (1/4)(12 inches)²
= 144 square inches.