Question

ABCD IS A QUADRILATERAL IN WHICH AB=AD,
ANGLE A =ANGLE C=90°
BC =8CM
SD=6CM
FIND AB AND CALCULATE THE AREA OF TRIANGLE ABD​

Answer 1

Answer:

Hence the length of AB is 5√2cm

Step-by-step explanation:

Given AB=AD,A=90°=C,BC=8 cm and CD=6 cm

BCD is a right triangle.

BD

2

=BC

2

+DC

2

[Pythagoras theorem]

BD

2

=8

2

+6

2

BD

2

=64+36

BD

2

=100

Taking square root on both sides,

BD=10cm

ABD is a right triangle.

BD

2

=AB

2

+AD

2

[Pythagoras theorem]

10

2

=2AB

2

[∵AB=AD]

100=2AB

2

AB

2

=100/2

AB

2

=50

Taking square root on both sides,

AB=√50

AB=√(2×25)

AB=5√2cm

Hence the length of AB is 5√2cm.