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Question

If ABCDE is a pentagon, then AB+AE+BC+DC+ED+AC equals

A
3AD
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B
3AC
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C
3BE
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D
3CE
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Solution

The correct option is B 3AC

In the pentagon ABCDE, join AC and AD.

By triangle law,

In ΔABC,

AB+BC=AC

In ΔACD,

AD+DC=AC

In ΔAED,

AE+ED=AD

Now,

AB+AE+BC+DC+ED+AC=(AB+BC)+(AE+ED)+DC+AC

=AC+(AD+DC)+AC

=AC+AC+AC

=3AC


991105_1057198_ans_124f8bc5604a4d0c8b1186cff255b9d8.png

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