|
Author |
Message |
|
TAGS:
|
|
|
Intern
Joined: 27 Apr 2003
Posts: 35
Followers: 0
Kudos [?]:
0
[0], given: 0
|
a parallelogram has 2 sides:14, 18 one of the diagonals is [#permalink]
 08 May 2003, 04:56
a parallelogram has 2 sides:14, 18 one of the diagonals is 16, what is the length of the othe diagonal?
jabs
|
|
|
|
|
|
|
Intern
Joined: 07 May 2003
Posts: 22
Followers: 0
Kudos [?]:
0
[0], given: 0
|
answer: 24
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
Joined: 03 Feb 2003
Posts: 1683
Followers: 4
Kudos [?]:
16
[0], given: 0
|
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.
|
|
|
|
|
|
Intern
Joined: 07 May 2003
Posts: 1
Location: US
Followers: 0
Kudos [?]:
0
[0], given: 0
|
If you use the above formula diagonal=28
|
|
|
|
|
|
SVP
Joined: 03 Feb 2003
Posts: 1683
Followers: 4
Kudos [?]:
16
[0], given: 0
|
so this should be the answer
|
|
|
|
|
|
Senior Manager
Joined: 02 Mar 2004
Posts: 372
Location: There
Followers: 1
Kudos [?]:
0
[0], given: 0
|
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
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
close
