SOLUTION: In the figure, rectangle ABCD is rotated 270° counterclockwise around point D to form rectangle EFGD. The perimeter of rectangle ABCD is 30 cm. How long is segment EC?

Algebra ->  Linear-equations -> SOLUTION: In the figure, rectangle ABCD is rotated 270° counterclockwise around point D to form rectangle EFGD. The perimeter of rectangle ABCD is 30 cm. How long is segment EC?       Log On


   

Question 946810: In the figure, rectangle ABCD is rotated 270° counterclockwise around point D to form rectangle EFGD. The perimeter of rectangle ABCD is 30 cm.

How long is segment EC?
_____cm
http://static.k12.com/calms_media/media/1572500_1573000/1572843/1/f02a772beb034a580c602cf7e19f5f0e9fe7baff/MS_IMC-141215-110508.jpg
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

if rectangle ABCD is rotated 270° counterclockwise around point D to form rectangle EFGD, dimensions of the ABCD and EFGD
given EF=9cm
the length of AB and DC equal to EF,so,
AB=DC=9cm
if the perimeter of rectangle ABCD is 30cm, then
2AB%2B2BC=30cm
AB%2BBC=15cm
9cm%2BBC=15cm
BC=15cm-9cm
BC=6cm => since BC equal to ED and FG,we have
ED=6cm and FG=6cm
since segment EC=ED%2BDC and since DC=9cm and ED=6cm, we have
EC=6cm%2B9cm
EC=15cm