Amr O.

asked • 09/10/14

In the parallelogram ABCD

m(<B)=60• ,it's perimeter=13cm and the length of the minor diagonal=3.5cm
find the length of AB and BC

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Phillip R. answered • 09/10/14

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when you combine the equations provided by Surendra you will get
 
x2 -6.5x +10 = 0 which you can factor into (x-4)(x-2.5) = 0
 
The original equation comes from the law of cosines
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Amr O.

Thanks for helping me I tried the law of cosines and got the two equations but couldn't solve them
so can you help by explaining how to solve them or combine them cuz I didn't understand
thanks again.
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09/10/14

Amr O.

 
oh thanks I got it now
from the first equation 
y=6.5-x
substitute in the second equation
we will get 3x2-19.5x+30=0
divide by 3 we will get x2-6.5x+10=0
by factorizing or the general formula we will get x=4 or x=2.5
if x=4 then y=6.5-4=2.5 and if x=2.5 then y=4
sorry cuz my brain stopped for a while and thank you for helping me making it work again :)
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09/10/14

SURENDRA K. answered • 09/10/14

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It is advisable that first you draw the figure.
 
Say, AB = x
       B C = y
 
Since perimeter = 13  cm
x + y =13/2=6.5
 
 
Applying the trigonometric identity---
 
Cos(60) =[x^2+y^2-(3.5)^2]/2xy
 
So, 
 
x^2+ y^2 -xy =  12.25
 
We have another equation as
 
x. + y =6.5
 
Solving these two equations
 
x = 4
 
y = 2.5
 
So,
AB =4 cm
BC = 2.5 cm
 
 
Any questions, welcome.
 
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Amr O.

I appreciate your answer but I have already got the two equations and couldn't solve them you made me sure that I use the right method but i need to know how to solve the equations thanks again
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09/10/14

SURENDRA K.

(x+ y)^2=6.5^2
 x^2 +y ^2+2xy =42.25
x^2+ y^2 =42.25-2xy
42.25-2xy=12.25+xy
3xy=30
xy=10
x-y=1.5
x+y=6.5
 
x=4
y=2.5
 
 
 
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09/10/14

SURENDRA K.

Hello Amr,
 
Yes, the solution of equations is not that straightforward here.
The two equations are
x + y = 6.5.    OR.   x^2+ y^2 +2xy =42.25
So,
x ^2+ y^2=42.25-2xy
Other equation is
x ^2 + y ^2 -xy=12.25
So,
42.25-2xy-xy=12.25
3xy =30
xy=10
(x-y)^2 =42.25-2xy-2xy=2.25
x-y=1.5
x+y=6.5
 
2x =8
x =4
y =2.5
 
Any other doubt?? Welcome
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09/10/14

SURENDRA K.

x+ y =6.5.    OR.   x^2 + y ^2 +2xy=42.25
 
x^2 + y^2 =42.25-2xy
 
Other equation is
 
x ^2+y^2-xy=12.25
42.25-2xy-xy=12.25
3xy=30
xy=10
 
(x-y)^2= x ^2+y^2-2xy=42.25-2xy-2xy=2.25
x-y=1.5
x+y=6.5
2x=8
x=4
y=2.25
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09/10/14

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