Question

Dete
Page No.
24 In the adjaring digun , LB-90%, LBAC = 6BC =CD =4am aand
AD- to.com do sin and moi.casa
tem
10 cm
to
4em
HINT AB?: (AB2-B02) - 36.cm2
.. Ababam
AC? (AB? +BC?)-52 cm2
. AC= 2 13 cm
Thus, AB = bem and AC= 2 13 cm​

Answer 1

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(b) Given ∠BAC = 90

∘

, ∠ ADC = 90

∘

,

AD=6cm,CD=8cm and BC=26cm.

(i) Δ ADC is a right triangle

∴AC

2

=AD

2

+DC

2

[ Pythagoras theorem]

∴AC

2

=6

2

+8

2

∴AC

2

=36+64

∴AC

2

=100

Taking square root on both sides,

AC=10cm

Hence length of AC is 10cm.

(ii) Δ ABC is a right triangle

∴BC

2

=AC

2

+AB

2

[ Pythagoras theorem]

∴26

2

=10

2

+AB

2

∴AB

2

=26

2

−10

2

∴AB

2

=676−100

∴AB

2

=576

Taking square root on both sides,

AB=24cm

Hence length of AB is 24cm.

(iii) Area of ΔABC =

1

/

2

×AB×AC

1

/

2

×24×10

= 120cm

2

Area of △ADC=1/2×AD×DC=1/2×6×8=24

Area of shaded region = area of ΔABC - area of ΔADC

= 120−24

= 96cm

2

Hence the area of shaded region is 96cm

2

Step-by-step explanation:

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