Answer:
Option C that is [tex]x=4,DF=EG=15[/tex] the right choice.
Step-by-step explanation:
Given,
A rectangle with the measures of its diagonal DF and EG.
Measure of diagonal DF = [tex]5x-5[/tex]
Measure of diagonal EG = [tex]x+11[/tex]
Note:Diagonal length of the rectangle are same.
So DF = EG
[tex]5x-5=x-11[/tex]
Subtracting [tex]x[/tex] and adding [tex]5[/tex] on both sides.
We have,
[tex]5x-x=11+5[/tex]
[tex]4x=16[/tex]
Dividing 4 both sides.
[tex]x=\frac{16}{4}=4[/tex]
So the value of [tex]x[/tex] is [tex]4[/tex].
Now plugging the value of [tex]x=4[/tex],we will find the numeric value of DF and EG.
DF = [tex]5x-5 =5(4)-5=15[/tex]
EG= [tex]x+11=4+11=15[/tex]
Both are equal DF = EG.
So x=[tex]4[/tex] and the length of diagonals are equal, DF = EG = [tex]15[/tex] unit.
