Question

given ab=17 cm bc =12cm cd=9cm angle bdc=90 degree angle acb =90degree. find the length of bd

Answer 1

Answer:

Consider Δ ABD

Using the Pythagoras theorem

AD2=AB2+BD2

By substituting the values

172=AB2+152

On further calculation

AB2=64

By taking out the square root

AB=64

So we get 

AB=8cm

We know that

Perimeter of quadrilateral ABCD=AB+BC+CD+AD

By substitution the values

Perimeter =8+12+9+17

By addition

Perimeter=46cm

We know that area of ΔABD=21×b×h

It can be written as:

Area of ΔABD=21×AB×BD

By substituting the values

Area of Δ ABC=21×8×15

On further calculation

Area of ΔABD=60cm2

Consider ΔBCD

We know thatBC=12cm,CD=9cmandBD=15cm

It can be written as a=12cm,b=9cmandc=15cm

So we get

s=2a+b+c

s=212+9+15