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
Answers
Answer:
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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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