Question

which equation would solve for x?
\\( \frac { 40 } { 48 } = \frac { 2 x + 7 } { 5 x - 2 } \\)
\\( \frac { 40 } { 48 } = \frac { 5 x - 2 } { 2 x + 7 } \\)
\\( \frac { 48 } { 40 } = \frac { 2 x + 7 } { 5 x - 2 } \\)

Explanation:

Step1: Recall the property of similar triangles

If two triangles are similar, the ratios of their corresponding sides are equal.

Step2: Identify the corresponding sides

In the given figure, assume the two triangles are similar. The ratio of one pair of corresponding sides is \(\frac{40}{48}\), and the ratio of another pair of corresponding sides is \(\frac{2x + 7}{5x-2}\).

Step3: Set up the proportion

Since the ratios of corresponding sides of similar triangles are equal, we get the equation \(\frac{40}{48}=\frac{2x + 7}{5x-2}\)

Answer:

\(\frac{40}{48}=\frac{2x + 7}{5x-2}\) (the first option)