Question

The length of the segment AD is 28 cm. The distance between the midpoints of segments AB and CD is 16 cm. Find the length of the segment BC .

Answer 1

Given=

length of the segment AD is 28 cm

distance between the midpoints of segments AB and CD is 16 cm

find out length of BC

To proof

AD = 28 cm

let the midpoint of the AB is E.

let the midpoint of the CD is F.

E & F are the midpoints i.e these points divide AB & CD in two equal parts.

Let BC = z

Let AE = EB = x     ( E is midpoint)

Let CF = FD = y      (F is midpoint)

the equation becomes

2x + 2y + z = 28

x + y + z = 16

mulitipy above equation by 2

we  get

2x + 2y + 2z = 32

thus solving the equations

2x + 2y + 2z = 32

2x + 2y + z = 28

we get

z = 4 cm

i.e BC = 4 cm

Hence proved