Question

find the unknown lengths for the similar triangles below.
image of two triangles: first with sides 5 m, 8 m, 11 m; second with sides 12 m, x, y
x = \boxed{} m (if needed, round to 2 decimal place.)
y = \boxed{} m (if needed, round to 2 decimal place.)
question 6
laptop computers are measured according to the diagonals of their screens.

Explanation:

Step1: Find the scale factor

The corresponding sides are 5 m and 12 m? Wait, no, wait. Wait, the first triangle has sides 5 m, 8 m, 11 m. The second triangle has a corresponding side to 5 m as 12 m? Wait, no, maybe the 5 m and 12 m are corresponding? Wait, no, similar triangles have corresponding sides proportional. So let's assume that the side of length 5 m in the first triangle corresponds to 12 m in the second triangle. So the scale factor \( k \) is \( \frac{12}{5} \).

Step2: Calculate \( x \)

The side of length 8 m in the first triangle corresponds to \( x \) in the second. So \( x = 8 \times \frac{12}{5} \)
\( x = \frac{96}{5} = 19.2 \)

Step3: Calculate \( y \)

The side of length 11 m in the first triangle corresponds to \( y \) in the second. So \( y = 11 \times \frac{12}{5} \)
\( y = \frac{132}{5} = 26.4 \)

Wait, wait, maybe I got the corresponding sides wrong. Wait, maybe the 5 m and 12 m are not corresponding? Wait, no, the triangles are similar, so the order of the sides should be corresponding. Let me check again. The first triangle: sides 5, 8, 11. Second triangle: 12, x, y. So the ratio of corresponding sides should be equal. So \( \frac{5}{12} = \frac{8}{x} = \frac{11}{y} \). Wait, that's another way. Let's do that.

So \( \frac{5}{12} = \frac{8}{x} \)
Cross-multiplying: \( 5x = 8 \times 12 \)
\( 5x = 96 \)
\( x = \frac{96}{5} = 19.2 \)

And \( \frac{5}{12} = \frac{11}{y} \)
Cross-multiplying: \( 5y = 11 \times 12 \)
\( 5y = 132 \)
\( y = \frac{132}{5} = 26.4 \)

Yes, that's correct. So the scale factor is \( \frac{12}{5} \) or \( \frac{5}{12} \)? Wait, no, if the first triangle's side is 5 and the second's is 12, then the scale factor from first to second is \( \frac{12}{5} \). So multiplying the first triangle's sides by \( \frac{12}{5} \) gives the second's. So 8 (12/5) = 19.2, 11 (12/5) = 26.4.

Answer:

\( x = 19.2 \) m, \( y = 26.4 \) m