Question

Use mid segment formula to find

a) x=
b) EF=
c) BC=
A
E
B
لی
3
D
4x+6
9x+4
F

Answer 1

• x = 5
• EF = 26
• BC = 49

Explanation:

Given midsegment EF = (4x+6) and base segment BC = (9x+4) of a trapezoid with base AD = 3, you want the value of x and the lengths of the two segments EF and BC.

Midsegment

The midsegment parallel to the base segment is the average of the lengths of the parallel bases.

4x +6 = 1/2((9x +4) +3))

8x +12 = 9x +7 . . . . . . . . . multiply by 2 and simplify

5 = x . . . . . . . . . . . . subtract 8x+7

Segments

Using this value of x, we find the lengths of the segments to be ...

EF = 4·5 +6 = 26

BC = 9·5 +4 = 49

Check

(BC +AD)/2 = EF

(49 +3)/2 = 52/2 = 26 . . . . as required

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