Question

30 points!! Please help me ASAP!! I don't understand this.

ABCD is a trapezoid with midsegment (EF). If AD=5x-11, EF=3x+7, BC=2x+7, how many units in length is (EF)?

Answer 1

`EF=61\ units`

Explanation:

we know that

In this problem, the length of the mid-segment EF is the sum of the two bases divided by 2

so

`EF=(1)/(2)(BC+AD)`

substitute the given values

`3x+7=(1)/(2)(2x+7+5x-11)`

Solve for x

`6x+14=(7x-4)`

`7x-6x=14+4`

`x=18`

Find the length of EF

`EF=3x+7`

substitute the value of x

`EF=3(18)+7`

`EF=61\ units`