Question

A rhombus and a square have the same base. If the diagonals of the rhombus measure $30cm$ and $16cm$, respectively, find the area of the square.

• A. $225c{m}^2$
• B. $200c{m}^2$
• C. $240c{m}^2$
• D. $289c{m}^2$

Answer 1

The correct option is D $289c{m}^2$

In a rhombus, the diagonals bisect each other at ${90}^0$
Referring the diagram, if $PR=30cm,SQ=16cm$, then $OP=15cm,OQ=8cm$
Since $△POQ$ is a right angled triangle,
${PQ}^2={OP}^2+{OQ}^2$

$=>{15}^2+8^2=289$
$=>PQ=\sqrt{289}=17$ cm
Hence, the length of the sides of the rhombus $=17$ cm.
Given, side of the square $=$ side of rhombus $=17cm$
Area of square ${side}^2=289{cm}^2$