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Quiz of the Month (May 2005)

Hector C. Parr

***

SOLUTION TO LAST MONTH'S QUIZ

  1.  28.284 cm
  2.  25.612 cm
  3.  26.042 cm
Notes. 
  1.  Crease is diagonal of 20 cm square.  

  2.  B'B2 = 252 + 202 = 1025
       So B'B = 32.01562
      Triangle YZX similar to BAB'
       So XY/XZ = B'B/B'A
      So XY = XZ.B'B/B'A = 25.612 

  3.  B'B2 = 152 + 202 = 625
       So B'B = 25 and MB = 12.5
      Triangle YMB similar to BAB'
       So MY/MB = BA/AB'
       Similarly MX/MB = AB'/AB
      So XY = MX + MY = MB.(BA/AB' + AB'/AB) = 26.042

THIS MONTH'S QUIZ

A ladder stands on level ground leaning against the vertical wall of a house. The foot of the ladder must stand outside the garden wall, which is 3 ft high and 3 ft from the house.

1. How long is the shortest ladder which can reach a point on the wall of the house 12 ft above the ground?

2. Alternatively, if the longest ladder available is only 12 ft long, then how far above ground level will be the highest point the ladder can reach?

3. With the data of question 2, how far is the foot of the ladder from the garden wall?
***

© Hector C. Parr (2005)

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