A blueprint is a scale drawing of a building. The dimensions of the blueprint for Patricia's dollhouse are 1/2 of the measurements of the actual dollhouse. The floor of the dollhouse has an area of 1,176 square inches. If the width of the dollhouse is 2/3 the length, what are the dimensions of the floor on the blueprint of the dollhouse?

_ inches by _ inches

The dimensions of the floor on the blueprint of Patricia's doll house are 21 inches by 14 inches, calculated by using the given area of the actual doll house and the ratio between its width and length.

Explanation:

To determine the dimensions of the blueprint of Patricia's doll house, we know the actual area of the doll house is 1,176 square inches and that the width is 2/3 of the length. Let's call the width w and the length l. Since w = (2/3)l, using the area formula for rectangles (area = length × width), we have:

1,176 = l × (2/3)l = (2/3)l²

Let's solve for l:

1,176 = (2/3)l²

(3/2) × 1,176 = l²

l² = 1,764

l = √1,764

l = 42 inches (since 42² = 1,764)

Now, find the width:

w = (2/3) × 42 = 28 inches

Since the blueprint's scale is half of the actual size, we need to divide both dimensions by 2 for the blueprint dimensions:

Blueprint length: 42 / 2 = 21 inches

Blueprint width: 28 / 2 = 14 inches

So, the dimensions of the floor on the blueprint of the doll house are 21 inches by 14 inches.