Answer:
Part A) [tex]x = 11[/tex]
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 [tex]m=\frac{base1+base2}{2}[/tex]
In provided figure, base1 is x+12 and base2 is 3x-4
A) solve for value of x
calculate the median [tex]m=\frac{base1+base2}{2}[/tex]
[tex]4x-18=\frac{x+12+3x-4}{2}[/tex]
[tex]4x-18=\frac{4x+8}{2}[/tex]
[tex]4x-18=2x+4[/tex]
[tex]2x-18=4[/tex]
[tex]2x = 18 + 4[/tex]
[tex]2x = 22[/tex]
[tex]x = 11[/tex]
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
