Question

A shown in the following figure, the area of square $ABCD$ is $16{cm}^2$ and the area of square CIPO is $9{cm}^2$. If $\overline{BC}\perp \overline{CO}$ then the length of $\overline{BO}=................cm$

• A. $7$
• B. $25$
• C. $625$
• D. $5$

Answer 1

The correct option is D $5$

Given : Area of square $ABCD=16c{m}^2$

Let sides of $ABCD$ and $CIPO$ be $x$ and $y$ respectively

But $A\left(\square ABCD\right)={\left(x\right)}^2$

$⟹16={\left(x\right)}^2⟹x=4=AB=BC=CD=DA$
Area of square $CIPO=9c{m}^2$

$y^2=9c{m}^2⟹y=3cm$

Now, in $△BCO,\angle C={90}^o$.

By pythagoras theorem,
${BC}^2+{OC}^2={BO}^2$
$⟹4^2+3^2={BO}^2$
$⟹{BO}^2=16+9=25$
$⟹BO=5cm$

Hence, the answer is $5$.