Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

In isosceles trapezoid $ABCD$ the median $MN$ cuts diagonals $AC$ and $BD$ at $P$ and $Q$, respectively. If $PQ$ is $4$ find the perimeter of the trapezoid. I found that $AC=BD=8$ and I know that $PQ$ is half of $AB-CD$ but I can't find $CD$. Any help would be appreciated. Angle A is 60 degrees. $MN$ is 8.

Edit: I wasn't given that $MN$ is 8. Now when I know that I can find the perimeter. $P=a+b+2(a-b)=32$

enter image description here

share|improve this question
    
Two diagonals from the same vertex $A$? –  enzotib Sep 26 '12 at 20:22
    
Sorry, my fault. The diagonals are AC and BD. OP edited. –  lam3r4370 Sep 26 '12 at 20:32
    
How exactly did you find that the length of the diagonals are $8$? –  EuYu Sep 26 '12 at 23:14
add comment

1 Answer

up vote 2 down vote accepted

The problem is ill-posed; the perimeter isn't determined by the given information. If we move $D$ and $C$ outward, as they come to lie vertically above $A$ and $B$, respectively, $P$ and $Q$ converge at the centre. Thus the trapezoid has to be scaled up without bounds for $PQ$ to retain the value $4$, and thus it can have arbitrarily large perimeters.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.