Problem 22 · 2014 Math Kangaroo
Hard
Geometry & Measurement
pythagorean-triple
The straight line \(g\) runs through the vertex A of the rectangle ABCD shown. The perpendicular distance from C to \(g\) is 2 and from D to \(g\) is 6. AD is twice as long as AB. Determine the length of AD.
Show answer
Answer: A — 10
Show hints
Hint 1 of 2
Set the line g through A as a direction and measure perpendicular distances of C and D from it.
Still stuck? Show hint 2 →
Hint 2 of 2
With AD = 2·AB the two distance equations combine into a tidy Pythagorean relation.
Show solution
Approach: coordinates with perpendicular-distance formulas
- Place A at the origin; write g by its unit normal. The distances of C and D from g are 2 and 6.
- Using AD = 2·AB, the distance conditions reduce to AD² = 6² + 8² = 100.
- So AD = 10.
Mark:
· log in to save