Question

(C) In figure (iii) given below, D = 90, AB = 16 cm, BC = 12 cm and CA = 6cm. Find CD.​

Answer 1

Answer:

3 1/6

Step-by-step explanation:

Given: D=90°,AB=16cm,BC=12cm and CA=6cm

ADC is a right triangle.

So, AC

2

=AD

2

+CD

2

[Pythagoras theorem]

6

2

=AD

2

+CD

2

…..(i)

ABD is also a right triangle.

So, AB

2

=AD

2

+BD

2

[Pythagoras theorem]

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 [from (i)]

36=112−24CD

24CD=112−36

24CD=76

CD=

24

76

=

6

19

∴CD=3

6

1

Hence the length of CD is 3

6

1 cm

Answer 2

Answer:

Given: D=90°,AB=16cm,BC=12cm and CA=6cm

ADC is a right triangle.

So, AC

2

=AD

2

+CD

2

[Pythagoras theorem]

6

2

=AD

2

+CD

2

…..(i)

ABD is also a right triangle.

So, AB

2

=AD

2

+BD

2

[Pythagoras theorem]

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 [from (i)]

36=112−24CD

24CD=112−36

24CD=76

CD=

24

7

=

6

19

∴CD=3

6

1

Hence the length of CD is 3

6

1

cm