Triangle ABC ~ triangle DEF.

Question

triangle ABC with side AB labeled 11, side CA labeled 7.6 and side BC labeled 7.9 and a second triangle DEF with side DE labeled 3.3

Determine the measurement of FD.
FD = 1.1
FD = 1.39
FD = 2.28
FD = 2.37

Answer 1

Since triangles ABC and DEF are similar (ABC ~ DEF), the ratios of their corresponding sides are equal.

We know the lengths of sides from triangle ABC:

• AB = 11
• CA = 7.6
• BC = 7.9

We also have the length of side DE from triangle DEF:

• DE = 3.3

We want to find the corresponding side FD in triangle DEF. Using the corresponding sides, we set up the ratio:

\[ \frac{AB}{DE} = \frac{FD}{BC} \]

We can rearrange this to solve for FD:

\[ FD = \frac{BC \cdot DE}{AB} \]

Now we can substitute in the values we have:

\[ FD = \frac{7.9 \cdot 3.3}{11} \]

Calculating the right-hand side:

1. Calculate \( 7.9 \cdot 3.3 \):

\[ 7.9 \cdot 3.3 = 26.07 \]

2. Now divide by 11:

\[ FD = \frac{26.07}{11} \approx 2.37 \]

So, the measurement of FD in triangle DEF is approximately 2.37.