Question

$ABCD$ is a rhombus. If the length of $AC$ and $BD$ are $16cm$ and $12cm$ respectively, then find the length of the sides.

• A. 10 cm
• B. 8 cm
• C. 6 cm
• D. 5 cm

Answer 1

The correct option is A 10 cm

Given $ABCD$ is a rhombus.
Hence, $AB=BC=CD=DA.$
Given, $AC=16cm$ and $BD=12cm.$
Since ABCD is a rhombus, the diagonals $AC$ and $BD$ will be perpendicular bisectors.
Hence, $AE=EC=8cm$ and $BE=ED=6cm.$

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

So, in the triangle $AEB,$ we have
$AE=8cm,BE=6cmand\angle AEB=90°$

By Pythagoreas Theorem,
$A{E}^2+B{E}^2=A{B}^2$
$\Rightarrow A{B}^2=8^2+6^2=64+36=100$
$\Rightarrow A{B}^2=100$
$\Rightarrow AB=10cm$
Hence, the sides of the rhombus are of length $10cm.$