Question

The lengths of the diagonals of a rhombus are 24 cm and 18 cm respectively. Find the length of each side of rhombus.
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Answer 1

Step-by-step explanation:

Explanation:-

Let ABCD be a rhombus whose diagonals AC and BD intersect at O.

Then, AC=24 cm and BD = 18 cm

Since the diagonals of a rhombus bisect each other,

We have:-

OA=OC=12 cm and OB=OD=9 cm

Again, the diagonals of rhombus bisect each other at right angles. So, ∠AOB = 90°

Let the length of each side of rhombus be x cm.

Then, in right angles ∆ AOB, by Pythagoras theorem, we have

AB²=OA²+OB²

x²=(12)²+(9)²

x²=144+81

x²=225

x=√225

x=15.

Hence, The length of each side of rhombus is 15 cm.

Answer 2

Given :-

The lengths of the diagonals of a rhombus are 24 cm and 18 cm respectively

To Find :-

Length of side

Solution :-

According to the pythagoras theorem

Let the rhombus be PQRS and O be the centre

Therefore

PO = OR (As diagonal bisect each other)

PO = 24/2 = 12 cm

Now

OQ = OS

OQ = 18/2 = 9 cm

Now, Using pythagoras theorem

H² = P² + B²

PS² = (12)² + (9)²

PS² = 144 + 81

PS² = 225

PS = √225

PS = 15 cm