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

Question

4 years ago

9

segment BC .

1 answer:

erastovalidia [21] · Answer 1 · 2022-01-19T00:58:22+03:00

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