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Question 40676: Hello, I am having difficulty understanding the Cartesian coordinate system. I apprecaite your help!!
An overhead light source projects parallelogram ABCD to another parallelogram below it labeled A'B'C'D'
One side of parallelogram ABCD, B to C is 3 units long. One side of the parallelogram A'B'C'D', B' to C' is 9 units long.
Please explain how the expression 6 + 2/3X represents the perimeter of the smaller ABCD paralleogram.
Thanks a million.
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! Hello, I am having difficulty understanding the Cartesian coordinate system. I apprecaite your help!!
An overhead light source projects parallelogram ABCD to another parallelogram below it labeled A'B'C'D'
IN SUCH A CASE THE PARALLELOGRAMS ARE SIMILAR AND THEIR SIDES WILL BE IN PROPORTION.THAT IS
AB/A'B'=BC/B'C'=CD/C'D'=DA/D'A'=K...AB=CD AND BC=DA..AND A'B'=C'D'..B'C'=D'A'
AB=K*A'B'....BC=K*B'C'
PERIMETER OF ABCD=2(AB+BC)...PERIMETER OF A'B'C'D'=2(A'B'+B'C')
One side of parallelogram ABCD, B to C is 3 units long. One side of the parallelogram A'B'C'D', B' to C' is 9 units long.
BC/B'C'=3/9=1/3=K
SO PERIMETER OF ABCD/PERIMETER OF A'B'C'D'=2(AB+BC)/2(A'B'+B'C')=2(K*A'B'+K*B'C')/2(A'B'+B'C')=K
BUT....K=1/3...AND BC=3....
PERIMETER OF ABCD =2(AB+BC)=2(AB+3)=6+2*AB
IF WE PUT A'B'=X..THEN AB=K*A'B'=X/3
SO PERIMETER OF ABCD = 6+2*AB=6+2*X/3
Please explain how the expression 6 + 2/3X represents the perimeter of the smaller ABCD paralleogram.
Thanks a million.
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