Question

4. The given figure shows a quadrilateral ABCD
in which AD = 13 cm, DC = 12 cm, BC = 3
cm and ZABD = ZBCD = 90°. Calculate the
А
length of AB.
B
D​

Answer 1

$\bigstar\:\:\underline{\sf AnsWer :} \: \bigstar$

From ΔDBC, using the pythagoras theorem,

$(DB)^{2}=(CD)^{2}+(BC)^{2}$

$(DB)^{2}=9+144=153$

Now, from ΔABD, using the Pythagoras theorem, we get

$(AD)^{2}=(AB)^{2}+(BD)^{2}$

Putting the value of $(DB)^{2}$,

$169=(AB)^{2}+153$

$(AB)^{2}=169-153$

$(AB)^{2}=16$

$AB=4cm$