Question

to the scaled copy?
3
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what is the length of the base in the scaled
copy?
? units
original
12
10
scaled copy
36
?

Explanation:

Step1: Find the scale factor

The scale factor is the ratio of the heights of the scaled - copy to the original. The height of the original is \(h_{1} = 12\), and the height of the scaled - copy is \(h_{2}=36\).
The scale factor \(k=\frac{h_{2}}{h_{1}}=\frac{36}{12}=3\).

Step2: Calculate the base of the scaled - copy

Let the base of the original be \(b_{1} = 10\). Since the figures are similar (because it's a scaled - copy), the ratio of the bases is the same as the ratio of the heights. Let the base of the scaled - copy be \(b_{2}\).
We know that \(\frac{b_{2}}{b_{1}}=k\). Substituting \(b_{1}=10\) and \(k = 3\) into the equation, we get \(b_{2}=k\times b_{1}\).
So \(b_{2}=3\times10 = 30\).

Answer:

\(30\)