A geometry problem by Pankaj Joshi

Geometry Level 2

In a parallelogram ABCD , the length AB and CD are both 4 units , the length of diagonal AC = 4 units , and the length of diagonal BD = 6 units . The length AD is equal to:

15 \sqrt {15} 10 \sqrt {10} 12 \sqrt {12} 20 \sqrt {20}

Pankaj Joshi by Pankaj Joshi , 23, India

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1 solution

Vaibhav Agarwal
Mar 1, 2014

CD=4, AC=4, length of median in triangle ACD (from D) = 6/2=3,

Thus from Apollonious theorem, A D 2 + C D 2 = 2. ( M E D I A N ) 2 + A C 2 / 2 AD^{2} + CD^{2} = 2.(MEDIAN)^{2} + AC^{2}/2 whcih implies A D 2 = 10 AD^{2} = 10 ..Hence A D = 10 AD = \sqrt{10}

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