Answer:
[tex] x = 6.25 [/tex]
Step-by-step explanation:
Given that ∆DFG ~ ∆RPQ, therefore, [tex] \frac{DF}{PR} = \frac{DG}{QR} = \frac{FG}{QP} [/tex] (similarity theorem).
DF = 10
PR = 8
DG = 5
QR = 4
QP = 5
FG = x
[tex] \frac{10}{8} = \frac{5}{4} = \frac{x}{5} [/tex]
Using [tex] \frac{5}{4} = \frac{x}{5} [/tex] , solve for x
cross multiply:
[tex] 4*x = 5*5 [/tex]
[tex] 4x = 25 [/tex]
[tex] x = \frac{25}{4} [/tex]
[tex] x = 6.25 [/tex]
