In figure (iii) given below, ZD = 90°, AB = 16 cm, BC = 12 cm and CA = 6cm.
Find CD.
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ADC
AC=2
AD2+cD2
D= 90°,AB= 16cm,BC= 12cmandCA= 6cm
6 2
AD2+CD2
ABD
AB2=AD2+BD2
16
2
=
AD
2
+
(BC+
CD)
2
16
2
=
AD
2
+
(12+
CD)
2
256=
AD
2
+
144+
24CD+
CD
2
256−
144=
AD
2
+
CD
2
+
24CD
AD
2
+
CD
2
=
112−
24CD
6 2
112−
24CD
36=
112−
24CD
24CD=
112−
36
24CD=
76
CD=
76/24=
19/6
∴
CD=
3
6
1
3
6
1
cm
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