Question

1. determine the missing side lengths of the triangles below. show your calculations.

a)
(there are two triangles: one labeled s, t, u with sides 7, 6.1, 8.4; the other labeled f, g, h with side 18.3, 25.2 and a missing side x)

Explanation:

Step1: Identify Similar Triangles

Triangles \( \triangle STU \) and \( \triangle FGH \) are similar (assumed by their proportional sides). First, find the scale factor. The side \( TU = 8.4 \) and \( GH = 25.2 \). The scale factor \( k=\frac{25.2}{8.4}=3 \).

Step2: Calculate Missing Side \( x \)

The corresponding side to \( x \) in \( \triangle STU \) is \( ST = 7 \). Using the scale factor, \( x = 7\times k = 7\times3 = 21 \). We can also verify with another side: \( SU = 6.1 \), \( FH = 18.3 \), and \( \frac{18.3}{6.1}=3 \), which confirms the scale factor.

Answer:

The missing side length \( x \) is \( 21 \).