Question

1. alfred wants to make a doll house that is a copy of his own house. the roof of his house is 10.8 m wide and is 2.4 m higher at the centre than the edges. if the doll house is 1.6 m wide, what will be the rise of the roof?

Explanation:

Step1: Set up proportion

Since the doll - house is a copy of the original house, the ratio of width to the rise of the roof is the same for both. Let the rise of the roof of the doll - house be $x$. The ratio for the original house is $\frac{10.8}{2.4}$, and for the doll - house is $\frac{1.6}{x}$. So we have the proportion $\frac{10.8}{2.4}=\frac{1.6}{x}$.

Step2: Cross - multiply

Cross - multiplying gives us $10.8x = 2.4\times1.6$.

Step3: Solve for $x$

First, calculate $2.4\times1.6 = 3.84$. Then $x=\frac{3.84}{10.8}=\frac{384}{1080}=\frac{16}{45}\approx0.36$ m.

Answer:

$\frac{16}{45}\text{ m}\approx0.36\text{ m}$