Question

What is the measure of line segment BE in the diagram below?

Answer 1

15

Explanation:

∆ABC ~ ∆AED, therefore,

`(AB)/(AE) = (BC)/(ED)`

Let BE = x

AB = x + 9

AE = 9

BC = 16

ED = 6

Plug in the values into the equation

`(x + 9)/(9) = (16)/(6)`

`(x + 9)/(9) = (8)/(3)`

Cross multiply

`(x + 9)(3) = (8)(9)`

`3x + 27 = 72`

Subtract 27 from each side

`3x = 72 - 27`

`3x = 45`

Divide both sides by 3

`x = (45)/(3)`

`x = 15`

Segment BE = x = 15