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# a parallelogram has 2 sides:14, 18 one of the diagonals is

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a parallelogram has 2 sides:14, 18 one of the diagonals is [#permalink]  08 May 2003, 03:56
a parallelogram has 2 sides:14, 18 one of the diagonals is 16, what is the length of the othe diagonal?

jabs
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explanation: calculate area of the triangle with sides 16,14,18 using hercules formula ie (area)^2=s(s-a)(s-b)(s-c) where s=(a+b+c)/2
so area=96.

this area=1/2*16*h (h is altitude- diagonals bisect each other, 16 base which is bisected by the altitude)
therefore h=12

other diagonal=2h=24
SVP
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another feature to remember:

for a parallelogram --- d1^2+d2^2=2*[a^2+b^2]

the sum of squares of diagonals equals to two sums of squares of sides.
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If you use the above formula diagonal=28
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so this should be the answer
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Let d1 and d2 be two diagonals.

d1^2 = a^2 + b^2 - 2ab cosA
d2^2 = a^2 +b^2 - 2ab cosB

A+B = 180, cosB = -cosA

d1^2 + d2^2 = 2(a^2+b^2)
16^2 + d2^2 = 2(14^2+18^2)

d2 = 28
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