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

Sadie Allen · Accepted Answer

FC = #16# cm

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#

James Atkins · Answer

undefined To find the length of segment FC, we need to understand that the perimeter of a parallelogram is the sum of all its side lengths.

Let's denote the length of segment EF as x. Since segment DE is 5 centimeters longer than segment EF, its length would be x + 5.

Now, since a parallelogram has opposite sides that are equal in length, segment DE is equal to segment FC. Therefore, the perimeter of the parallelogram can be expressed as:

Perimeter = DE + EF + FC + DC

Given that the perimeter is 54 centimeters, and DE is equal to FC, we can rewrite the equation as:

54 = (x + 5) + x + FC + DC

Now, we substitute the known values into the equation:

54 = (x + 5) + x + FC + (x + 5)

Simplify the equation:

54 = 3x + 10 + FC

Now, isolate FC:

FC = 54 - 3x - 10

FC = 44 - 3x

So, the length of segment FC is 44 - 3x centimeters.