ABCD is a parallelogram a perpendicular BC and CA perpendicular a d is a b equals to 8 cm and C is equals to 10 cm find a b is equals to 8 cm
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As AD
is drawn perpendicular to
BC in right angled ΔABC
, it is apparent that ΔABC
is right angled at ∠A
as shown below (not drawn to scale).
enter image source here
As can be seen
∠B is common in
ΔABC as well as ΔDBA
(here we have written two triangles this way as
∠A=∠D
, ∠B=∠B
and ∠C=∠BAD ) - as both are right angled (obviously third angles too would be equal) and therefore we have
Δ
A
B
C
≈
Δ
D
B
A
and hence
B
C
A
B
=
A
B
B
D
=
A
C
A
D
..............(1)
therefore, we have
B
C
A
B
=
A
B
B
D
or
A
B
2
=
B
C
×
B
D
=
9
×
4
=
36
Hence
A
B
=
6
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