The perimeter of parallelogram CDEF is 54 centimeters. Find the length of segment FC if segment DE is 5 centimeters longer than segment EF? (Hint: Sketch and label a diagram first.)

Question

4026 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-15T13:26:10

FC = #16# cm enter image source here

See the attached diagram:

EF = #x# cm
DE = #x + 5# cm
DC = EF
DE = FC

Perimiter,#p# = #2 (a + b)# = # 2(EF + DE)#

#54 = 2(x + x+5)#
#54 = 2(2x+5)#
#54 = 4x+10#
#54-10 = 4x#
#44=4x#
#x=44/4#
#x=11#
That means Side DE = #x+5# = #11+5 = 16# cm

Since Side DE = FC, therefore FC = #16# cm

Checking the answer:
#2(11 + 16)#
#2xx27=54#