Question

8.2.4 cor
created p
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7
the triangles displayed are scaled copies of one another.
a. find the scale factor
b. what is the value of x?

Explanation:

Step1: Calculate the scale factor

The scale factor \(k\) is found by dividing the corresponding side of the larger triangle by the smaller one. For the base sides, \(k=\frac{10}{4}\).

$$k = \frac{10}{4}=\frac{5}{2}=2.5$$

Step2: Find the value of \(x\)

Since the triangles are scaled copies, we use the scale factor. We know that \(\frac{25}{x}=k\) (or \(x\times k = 25\)). Substitute \(k = 2.5\) into the equation \(x\times2.5=25\). Then \(x=\frac{25}{2.5}\).

$$x=\frac{25}{\frac{5}{2}}=25\times\frac{2}{5}=10$$

Answer:

a. \(2.5\)
b. \(10\)