In the diagram below, QR is perpendicular to BD
Find the length of BD.
If entering your answer as a decimal, round your final answer to the nearest hundredth.

24

Step-by-step explanation:

Lines QR and BD are perpendicular.

Angles RQB and RQD are right angles.

Angles AQB and AQR are complementary.

Angles CQD and CQR are complementary.

Angles AQR and CQD are congruent.

That makes angles AQB and CQD congruent.

Angles B and D are both right angles, so they are congruent.

Triangles AQB and CQD are similar triangles by AA Similarity.

Corresponding sides of similar triangles have proportional lengths.

AB/BQ = CD/DQ

32/15 = 19.2/DQ

32DQ = 15 * 19.2

DQ = 9

BD = BQ + DQ = 15 + 9 = 24

BD = 24

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so, converting firstly the mixed fractions to improper fractions and then "adding".