Question

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..

Answer 1

Hey there,

Given in triangle ABC, XY is a horizontal line as : XY║BC
∠ABC = 90°

AB = 12cm
AY = 8cm
and
$\frac{AX}{XB} = \frac{1}{2}$

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, $\frac{AX}{XB} = \frac{1}{2}$ So we can say that $\frac{AY}{YC} = \frac{1}{2}$
then we get $\frac{8}{YC} = \frac{1}{2}$

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 = $\sqrt{432$
So,
AC = 24cm and BC = 20.7846cm as your answer

Hope this helps!

Answer 2

Answer:

Hope it helps!!!

plz mark brainliest and follow me