Question

The length of the diagonals of a rhombus are 30 cm and 40 cm find the side of the rhombus

Answer 1

Consider a rhombus ABCD whose AC = 30 cm and BD = 40 cm. Let AC and BD intersect at a point O

It is known that the diagonals of a rhombus are perpendicular to each other

∴ ∠AOB = 90°

Using Pythagoras theorem in ∆AOB

AB2 = OA2 + OB2 = (15 cm)2 + (20 cm)2 = (225 + 400) cm2 = 625 cm2 = (25 cm)2

⇒AB = 25 cm

Thus, the side of the rhombus is 25 cm

Answer 2

$\huge \underline \mathbb {SOLUTION:-}$

As diagonals of a rhombus are equal and cut each other at right angle.

• Figure provided in the above attachment.

Using Pythagoras theorem:

• AD² = AO2² + OD²

➠ AD² = (30/2)² + (40/2)²

➠ AD² = 15² + 20²

➠ AD² = 225 + 400

➠ AD² = 625

➠ AD = √625

➠ AD = 25 cm

• So, side of the rhombus is 25 cm.

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\end{picture}$