A blueprint is a scale drawing of a building. The dimensions of the blueprint for Penny's doll house are 1/4 of the measurements of the actual doll house. The floor of the doll house has an area of 864 sq inches. if the width of the doll house is 2/3 the length, what are the dimensions of the floor on the blueprint of the doll house?
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If the length is x, then the width is 2/3 x. So, the area is
2/3 x^2 = 864
x = 36
Now you know the doll house is 24x36 inches
Divide those by 4 to get the drawing's dimensions.
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To find the dimensions of the floor on the blueprint of the dollhouse, we need to follow these steps:
Step 1: Let's assume the length of the dollhouse is "L" inches.
Step 2: Since the width of the dollhouse is 2/3 the length, we can calculate the width as (2/3)L.
Step 3: We know that the area of the floor of the dollhouse is 864 square inches. The area of a rectangle is given by the formula: Area = Length × Width.
Step 4: Plugging in the values, we have 864 = L × (2/3)L.
Step 5: To simplify the equation, we can eliminate the fraction by multiplying both sides by 3, resulting in 2592 = 2L².
Step 6: To solve for L, we divide both sides by 2, giving us L² = 1296.
Step 7: Taking the square root of both sides, we get L ≈ 36.
Step 8: Now that we know the length of the dollhouse is 36 inches, we can calculate the width as (2/3) × 36, which is approximately 24 inches.
Step 9: Finally, since the dimensions of the blueprint are 1/4 of the actual dollhouse, we need to find 1/4 of the length and width dimensions. The length on the blueprint will be (1/4) × 36 = 9 inches, and the width will be (1/4) × 24 = 6 inches.
Therefore, the dimensions of the floor on the blueprint of the dollhouse are approximately 9 inches by 6 inches.