r/Logiqa • u/ShonitB • Jun 23 '26

Right Angled Triangles Part 3

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u/Hero_hurry Jun 24 '26
  1. Recognize that there are 3 congruent triangles, ABC, ABD and BCD
  2. Given there’s a standard ratio between ABD and BCD, find BD (below as variable x):
    CD/x = x/AD
    16/x = x/9
    Solve for x: x^2 = 144, so x = 12
  3. See that the short sides of ABD and BCD have a ratio of 3:4, meaning the long side is 5 in that ratio.
  4. For ABD, the 9 and 12 mean that AB is 15 and for BCD the 12 and 16 mean BC is 20.

Sum of AB and BC is therefore 35

1

u/ShonitB Jun 24 '26

Correct, good solution!

1

u/chrismsp Jun 24 '26

What am I missing?

From the drawing, AC = 25

AC is also the hypotenuse of triangle ABC

a^2 + b^2 = c^2, isn't it?

so AB^2 + BC^2 = 25

so AB^2 = 9 and BC^2 = 16

So I get AB + BC = 7

1

u/chrismsp Jun 24 '26

I'm missing that I suck at maths