Question

A wire when bent in the form of a square encloses an area $=576c{m}^2$. Find the largest area enclosed by the same wire when bent to form a rectangle whose adjacent sides differ by $4cm$.

• A. $572c{m}^2$
• B. $472c{m}^2$
• C. $302c{m}^2$
• D. $506c{m}^2$

Answer 1

The correct option is A $572c{m}^2$

Given: A wire when bent in the form of a square encloses an area $=576c{m}^2$

We know Area of square $={\left(\text{side}\right)}^2$

${\left(\text{side}\right)}^2=576$

$\text{side}=24cm$

And

We know perimeter of square $=4\times \text{side}=4\times 24=96cm$

And now the same wire when bent to form a rectangle whose adjacent sides differ by $4cm$.

So, Let length of formed rectangle $=x$ and breadth of rectangle $=x-4$

And we know perimeter of rectangle $=2(\text{Length}+\text{Breadth})$, so we get

$\Rightarrow 2(x+x-4)=96$

$\Rightarrow 2(2x-4)=96$

$\Rightarrow 2x-4=48$

$\Rightarrow 2x=52$

$\Rightarrow x=26$

So length of formed rectangle $=26cm$

And Breadth of Rectangle $=26-4=22cm$

And Area of Rectangle $=26\times 22=572c{m}^2$