In the given figure, angleB = 90°, XY // BC, AB = 12 cm, AY = 8 cm and AX : XB = 1 : 2. Find the lengths of AC and BC.
Class- 9
Chapter- Pythagoras Theorem
Expect for content quality answers..
Class- 9
Chapter- Pythagoras Theorem
Expect for content quality answers..
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Verified answer
Hey there,Given in triangle ABC, XY is a horizontal line as : XY║BC
∠ABC = 90°
AB = 12cm
AY = 8cm
and
We know from side splitter theorem if a line is Parallel to a side of a triangle and intersect the other two sides, then this line divides those two sides proportionally.
As we know,
then we get
YC = 16, So AC = 8 + 16 = 24cm
Now, apply Pythagoras theorem in triangle ABC
(ABC)² = (AB)² + (BC)²
⇒ ( 24)² = (12)² + (BC)²
⇒ (BC)² = 576 - 144
⇒ (BC)² = 432
⇒ BC =
So,
AC = 24cm and BC = 20.7846cm as your answer
Hope this helps!