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.)
a)14
b)44
c)16
d)11
To find the length of segment FC in parallelogram CDEF, we can follow these steps:
Step 1: Sketch and label a diagram
Start by drawing a parallelogram CDEF. Label the sides with their lengths: FC, CD, DE, and EF. Keep in mind that opposite sides of a parallelogram are equal in length.
Step 2: Write down the given information
The perimeter of parallelogram CDEF is 54 centimeters, which means the sum of all four sides is 54 cm. So, we have:
FC + CD + DE + EF = 54
Step 3: Express the length EF in terms of FC
We are given that segment DE is 5 centimeters longer than segment EF. So, we can write:
DE = EF + 5
Step 4: Apply what we know about the properties of a parallelogram
Opposite sides of a parallelogram are equal in length. So, we can write:
FC = DE
Substituting the expressions for DE and EF from steps 3 and 4 into the equation from step 2, we have:
FC + CD + (EF + 5) + EF = 54
Step 5: Simplify and solve for FC
Combine like terms:
2EF + FC + CD + 5 = 54
Now, we need to use the fact that the perimeter of a parallelogram is equal to the sum of all four sides. We know that CD = EF, so we can rewrite the equation as:
2EF + 2FC + 5 = 54
Simplify further:
2EF + 2FC = 54 - 5
2EF + 2FC = 49
Divide both sides by 2:
EF + FC = 24.5
Now, we know that EF = FC since opposite sides of a parallelogram are equal. So we have:
FC + FC = 24.5
2FC = 24.5
Divide both sides by 2:
FC = 24.5 / 2
FC = 12.25
Therefore, the length of segment FC is approximately 12.25 centimeters.
Since none of the given answer choices match the calculated length, there might be a mistake in the provided options or the calculations. Please double-check the options or review the steps to ensure accuracy.
let the width be x
then the length is x+5
solve....
2x + 2(x+5) = 54