Quant Question Of The Day: 27
[latexpage]
Geometry
The diagonals AC and BD of quadrilateral ABCD are perpendicular to each other. If AB = 3, BC = 4 , CD = 5 , find the length of AD.
If intersection point is P, then
AP² + BP² = AB²
BP² + CP² = BC²
CP² + DP² = CD²
DP² + AP² = AD²
we can see that AD² + BC² = AB² + CD²
AD = √(3² + 5² – 4²) = 3√2
3√2
3 under root 2
3root2 (using Pythagoras theorems in all triangles)
3 root 2