Question

Both angle XAB and angle XYZ are right angles, XB = 6, BY = 2 and AB = 4.
The ratio of the area of triangle XAB/ area of triangle XYZ is
(a) 3/5
(b) 5/16
(c) 9/25
(d) 4/5
(e) 3/25

Answer 1

Need the picture to do this... :\

Answer 2

Use ratio of similar figures...
triangle XAB is similar to triangle XYZ (AAA)
By Pyth thm, \(XA=\sqrt{XB^2 - AB^2} = \sqrt{6^2 - 4^2}=\sqrt{20}\)
ratio of areas = (ratio of sides)^2
So,
\[\frac{\text{area of triangle XAB}}{\text{area of triangle XYZ}} \ = \ (\frac{XA}{XY})^2\]\[\frac{\text{area of triangle XAB}}{\text{area of triangle XYZ}} \ = \ (\frac{\sqrt{20}}{6+2})^2\]Time for you to work out the answer!