Answer:
BD = 24
Step-by-step explanation:
EF = 44 - 8x,
BD = 44 - 5x.
Since EF is a midsegment of ∆BCD, therefore, based on the Midsegment Theorem,
[tex] EF = \frac{1}{2}(BD} [/tex]
[tex] 44 - 8x = \frac{1}{2}(44 - 5x} [/tex]
Multiply both sides by 2
[tex] 2(44 - 8x) = 44 - 5x [/tex]
[tex] 88 - 16x = 44 - 5x [/tex]
Collect like terms
[tex] 88 - 44 = 16x - 5x [/tex]
[tex] 44 = 11x [/tex]
Divide both sides by 11
[tex] 4 = x [/tex]
x = 4
BD = 44 - 5x
Plug in the value of x
BD = 44 - 5(4) = 44 - 20
BD = 24
