Question

scale factors
the shapes in each pair are similar. find the value of x
1)
the value of x = ______
2)
the value of x = ______
3)
the value of x = ______
4)
the value of x = ______
5)
the value of x = ______
6)
the value of x = ______
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Explanation:

1)

Step1: Find scale factor

The ratio of corresponding sides: $\frac{6}{2} = 3$.

Step2: Apply to base

Set up proportion: $\frac{x + 6}{3} = 3$. Solve: $x + 6 = 9 \implies x = 3$.

Step1: Find scale factor

$\frac{2.5}{5} = 0.5$.

Step2: Apply to length

$\frac{5}{x + 6} = 0.5 \implies x + 6 = 10 \implies x = 4$.

Step1: Find scale factor

$\frac{9}{6} = 1.5$.

Step2: Apply to base

$\frac{12}{2x + 2} = 1.5 \implies 2x + 2 = 8 \implies 2x = 6 \implies x = 3$.

Answer:

3

2)