Question

the length of AB=12cm, CD=4cm,AC =13cm.If

∠ABD is 900 , find the length of AD.
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Answer 1

Answer:

Given AB=12cm,AC=13cm,CE=10cmandDE=6cm

ABC is a right triangle.

AC2=AB2+BC2[Pythagoras theorem]

132=122+BC2

BC2=132−122

BC2=169−144

BC2=25

Taking square root on both sides,

BC=5cm

CDE is a right triangle.

CE2=CD2+DE2[Pythagoras theorem]

102=CD2+62

100=CD2+36

CD2=100−36

CD2=64

Taking square root on both sides,

CD=8cm

BD=BC+CD

BD=5+8

BD=13cm

Hence the length of BD is 13cm