But What About The Angles Between Them?

Geometry Level 2

In the quadrilateral $ABCD$ , we are given the side lengths $AB=5$ , $BC=17$ , $CD=5$ and $DA=9$ . If $BD$ is an integer, what is the measure of $BD$ ?

11 12 13 14 15 16 17

2 solutions

Mateo Matijasevick
Apr 11, 2016

Applying Triangular Inequality to $\triangle ABD$ , $9+5>BD$ , thus, $14>BD$ . Now, from $\triangle CBD$ , we have that $5+BD>17$ , therefore $BD>12$ . The only integer that is between $12$ and $14$ is $13$ . Hence, $BD=13$ .

Nice. I never thought about it that way =)

Finn C - 5 years, 2 months ago

nice solution :D Upvoted

Syed Baqir - 5 years, 2 months ago

Simone De Vita
Apr 12, 2016

We have two triangles, BD must be: BD>4 BD<14 BD>12 BD<22

so 12 < BD < 14 Since BD is an integer it must 13

can you include the complete solution how you got these limits !

thanks

Syed Baqir - 5 years, 2 months ago

But What About The Angles Between Them?

2 solutions

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