Question

In the given figure angle B. = 90° find the length of BC​

Answer 1

where is the figure

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Answer 2

Explanation:

Correct option is

B

AC=24 cm and BC=12

3

cm.

Given: XY∥BC, ∠B=90

∘

, AX:XB=1:2

And, AB=12 cm, AY=8 cm

Now,

XB

AX

=

2

1

⇒

AB−AX

AX

=

2

1

⇒2AX=AB−AX

⇒3AX=AB

⇒3AX=12 cm

⇒AX=4 cm

Now, In △AXY and △ABC

∠XAY=∠BAC (Common)

∠AXY=∠ABC (Corresponding angles)

∠AYX=∠ACB (Corresponding angles)

Thus, △AXY∼△ABC (AAA rule)

Hence,

AB

AX

=

AC

AY

⇒

12

4

=

AC

8

⇒AC=

4

8×12

⇒AC=24

Hence, AC=24 cm

Now, applying Pythagoras theorem in △ABC,

AC

2

=AB

2

+BC

2

⇒24

2

=12

2

+BC

2

⇒BC

2

=24

2

−12

2

⇒BC

2

=432

⇒BC=

432

⇒BC=12

3

Hence, BC=12

3

cm