Question

The diagonals of a rhombus are 24cm and 10cm. Find the length of the side of a rhombus​

Answer 1

Step-by-step explanation:

Let ABCD be a rhombus, in which AB=BC=CD=DA

and diagonalAC=10cm and diagonalBD=24cm bisect each other.i.e., OA and OC are half of AC and BO and OD are half of BD.

Therefore, the distance of OA=OC=10/2=5cm.

BO=OD=24/2=12cm.

In each triangles angle O=90°.

In triangle AOB, angleO=90°.

By Pythagoras theorem:

AB²=OB²+OA²

AB²=12²+5²=144+25=169

AB=√169=13cm.

Each side of rhombus is 13cm.

Answer 2

☆ SIDE = 13cm

REFER THE ATTACHMENT

GIVEN

Diagonal 1 = 24 cm

Diagonal 2 = 10 cm

TO FIND

Measure of it's side

CALCULATION

As diagonals bisect perpendicularly in a Rhombus,

The portion OA & OB will be half of the diagonals .

Consider the Right Angle ∆ AOB

OA = 12 cm

OB = 5 cm

(AB)² = 12² + 5² ⇨ Right angle Triangle

12² + 5² = Hypotenuse²

144 + 25 = Hypotenuse²

169 = Hypotenuse²

√169 = Hypotenuse

13 = Hypotenuse

SOLUTION

Hypotenuse = Rhombus's side = AB = 13 cm

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