Question

ABCD is rhombus. If the length of AC and BD are 8 cm and 6 cm respectively, then find the length of the sides.

• A. 3 cm
• B. 4 cm
• C. 5 cm
• D. 6 cm

Answer 1

The correct option is C 5 cm

Given ABCD is a rhombus.
Hence, AB = BC = CD = DA.

Given, AC = 8 cm and BD = 6 cm.

Since, ABCD is a rhombus, the diagonals AC and BD will be perpendicular bisectors.
Hence, AE = EC = 4 cm and BE = ED = 3 cm.

Now, we know that,
$\angle AEB=\angle BEC=\angle CED=\angle DEA=90°$

So, in the triangle AEB,
$AE=4cm,BE=3cmand\angle AEB=90°$

By Pythagoreas Theorem,
$A{E}^2+B{E}^2=A{B}^2\Rightarrow A{B}^2=4^2+3^2=16+9=25\Rightarrow A{B}^2=25\Rightarrow AB=5cm$

Hence, the sides of the rhombus are of length 5 cm.