XYZ is an isosceles triangle such that XY = YZ = 15 cm and angle XYZ = 90°. What is the length of the perpendicular drawn from Y on XZ?
Answer & explanation
Correct answer: option 4
(XY)2 + (YZ)2 = (XZ)2 → Pythagoras theorem
(15)2 + (15)2 = (XZ)2
225 + 225 = (XZ)2
450 = (XZ)2
Therefore,
XZ = 15\(\sqrt{2}\)
Area of Δ with base YZ = Area of Δ with base XZ
⇒\(\frac{1}{2}\) × 15 × 15 = \(\frac{1}{2}\) × YS × 15\(\sqrt{2}\)
⇒ YS =\(\frac{15}{\sqrt {2}}\)