Question

In the adjoining figure, AC = 50 cm, BD = 120 cm. O is the midpoint of
AC and BD . Find the length of AB and CD. Are they equal?
​

Answer 1

Answer:

AB = CD = 65cm.

Step-by-step explanation:

As O is the mid point of AC and BD,

AO = 1/2 of AC and AO = OC.

BO = 1/2 of BD and BO = OD.

In triangle AOB amd COD,

Angle O = Angle O (Comman = 90⁰)

AO = OC ( O is the mid point of AC)

DO = OB (O is the mid point of BD)

By SAS property, triangle AOB is congruent to triangle COD.

CD = AB (By CPCT)

Thus AB and CD are equal.

In triangle AOB,

Angle O = 90⁰, OB = 1/2 ×120 = 60cm, OA = 1/2 × 50 = 25cm.

By Pythagoras Theorum, AB² = OA² + OB².

AB² = 25² + 60²

AB² = 625 + 3600

AB² = 4225

AB² = 65 × 65

AB² = 65²

AB = 65cm.

In triangle DOC,

Angle O = 90⁰, OD = OB = 60 cm , OC = OA = 25cm.

By Pythagoras Theorum, CD² = OC² + OD².

CD² = 25² + 60²

CD² = 625 + 3600

CD² = 4225

CS² = 65 × 65

CD² = 65²

CD = 65cm.