Find the scale factor and solve for x in the given problems. Triangles are similar.

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the visible problems:

1. Find the scale factor.
To find the scale factor, we compare the lengths of corresponding sides of the two similar triangles.

Identify corresponding sides.
The smaller triangle has sides 6, 8, and 10.
The larger triangle has sides 12, 16, and 20.
Calculate the ratio of corresponding sides.
Ratio of vertical sides: $\frac{12}{6} = 2$
Ratio of horizontal sides: $\frac{16}{8} = 2$
Ratio of hypotenuses: $\frac{20}{10} = 2$

Since all ratios are equal, the scale factor is 2.

The scale factor is $\boxed{2}$ .

2. Solve for x. $\frac{2}{x} = \frac{6}{7}$ . Give your answer as a common fraction.
Cross-multiply the fractions.
$2 \times 7 = 6 \times x$ $14 = 6x$
Isolate $x$ by dividing both sides by 6.
$\frac{14}{6} = x$
Simplify the fraction.
$x = \frac{14 \div 2}{6 \div 2}$ $x = \frac{7}{3}$
The value of $x$ is $\boxed*{\frac{7}{3}*}$ .

3. Find the length of x in the similar triangles below.
The image for this question is incomplete, as the triangles are not visible. Please provide the full image for this problem.

Answer