The lengths of the diagonals of a rhombus are 24 cm and 10 cm. Find each side of the rhombus.
Answers
SOLUTION :
GIVEN : Diagonals of a rhombus are 24 cm & 10 cm.
Let ABCD be a rhombus with diagonals AC = 10 cm and BD = 24 cm.
We know that diagonal of a rhombus bisect each other at 90°. AO = OC & OB = OD & ∠AOB = ∠AOD = ∠BOC = ∠COD = 90°.
Therefore, AO = OC = 5 cm and BO = OD = 12 cm.
In ∆AOB,
AB² = OA² + OB²
[By using Pythagoras theorem]
AB² = 5² + 12²
AB² = 25 + 144
AB² = 169
AB = √169
AB = 13 cm.
Hence, the length of the each side of the rhombus is 13 cm.
HOPE THIS ANSWER WILL HELP YOU...
Answer:
Step-by-step explanation:
Given :-
Diagonals of a rhombus are 24 cm and 10 cm.
To Find :-
Side of the rhombus.
Solution :-
Let ABCD be the rhombus.
And AC and BD intersect each other at O.
AO = 1/2 × 10 = 5 cm
BO = 1/2 × 24 = 12 cm
In right angled △AOB,
By applying Pythagoras theorem, we get
AB² = AO² + BO²
⇒ AB² = 5² + 12²
⇒ AB² = 25 + 144
⇒ AB² = 169
⇒ AB = √169
⇒ AB = 13 cm.
Hence, the length of the each side of the rhombus is 13 cm.