Question

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?​

Answer 1

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,

$EF = \frac{1}{2}(BD}$

$44 - 8x = \frac{1}{2}(44 - 5x}$

Multiply both sides by 2

$2(44 - 8x) = 44 - 5x$

$88 - 16x = 44 - 5x$

Collect like terms

$88 - 44 = 16x - 5x$

$44 = 11x$

Divide both sides by 11

$4 = x$

x = 4

BD = 44 - 5x

Plug in the value of x

BD = 44 - 5(4) = 44 - 20

BD = 24