Question

EF is the median of trapezoid ABCD.

Answer 1

Answer:

Part A) $x = 11$

B) length of BC =  x + 12 =  x + 12 = 11 + 12 =23

length of EF =  4x - 18 =  4(11) - 18 = 44 - 18 =26

length of AD =  3x - 18 =  3(11) - 4 = 33 - 4 =29

Step-by-step explanation:

Median of trapezium is $m=\frac{base1+base2}{2}$

In provided figure, base1 is x+12 and base2 is 3x-4

A) solve for value of x

calculate the median $m=\frac{base1+base2}{2}$

$4x-18=\frac{x+12+3x-4}{2}$

$4x-18=\frac{4x+8}{2}$

$4x-18=2x+4$

$2x-18=4$

$2x = 18 + 4$

$2x = 22$

$x = 11$

B) To find the length of BC, AD and EF , put the value of x in equation of lines

length of BC =  x + 12 =  x + 12 = 11 + 12 =23

length of EF =  4x - 18 =  4(11) - 18 = 44 - 18 =26

length of AD =  3x - 4 =  3(11) - 4 = 33 - 4 =29