Question

The given figure shows a quadrilateral ABCD in which AD=13cm ,DC=12cm,BC=3cm
and ANGLE ABD =ANGLE BCD= 90. calculate the length of AB

Answer 1

In the triangle DBC

${db }^{2} = {dc}^{2} + {bc }^{2}$
${db}^{2} = {12}^{2} + {3 }^{2} =153.$
In triangle DBA
${ad}^{2} = {db}^{2} + {ab}^{2}$
${13}^{2} = 153 + {ab}^{2}$
${ab}^{2} = 169 - 153 = 16$
$ab = \sqrt{16} = 4$
.'. ab=4cm

Answer 2

Answer:

AB= 4cm

Step-by-step explanation:

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 $(DB)^{2}$,

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

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

$(AB)^{2}=16$

$AB=4cm$