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In the diagram below of triangle BCD, E is a midpoint of BC and F is a midpoint of CD. If EF = 44 - 8x, and BD = 44 - 5x, what is the measure of BD?​

In the diagram below of triangle BCD E is a midpoint of BC and F is a midpoint of CD If EF 44 8x and BD 44 5x what is the measure of BD class=

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akposevictor

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

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