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.)

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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:
$2(11 + 16)$
$2xx27=54$