Question

4. The given figure shows a quadrilateral ABCD
in which AD = 13 cm, DC = 12 cm, BC= 3cm and <ABD = <BCD = 90° . Calculate the length of AB.​

Answer 1

Step-by-step explanation:

∠BCD=90

Thus,

BD ^2 = BC ^2 + CD^2 (Pythagoras theorem)

BD ^2 = 12 ^2 + 3 ^2

BD ^2 =144+9

BD=√153

Now, In △ABD, ∠ABD=90 °

AD ^2 =BD ^2 + AB ^2

13 ^2 =( √153 ) ^2 +AB ^2

169=153+AB ^2

16=AB ^2

AB=4 cm