Question

A wire when bent in the form of a square encloses an area $676c{m}^2$. Find the largest area enclosed by the same wire when bent to form a rectangle whose adjacent sides differ by $4cm.$

• A. $672c{m}^2$
• B. $672m^2$
• C. $6.72c{m}^2$
• D. $67.2c{m}^2$

Answer 1

The correct option is A $672c{m}^2$

Let $x$ be the side of the square.

The area of the square $=x^2$

Given, the area of square $=576c{m}^2$

$\therefore x^2=576⟹x=26$

Now, the length of the wire = perimeter of the square with side as $26cm=4x=4\times 26=104cm$

Let $y$ be the length of the rectangle.

$\therefore$ breadth of the rectangle $=y-4$

Since the same wire is used to bend in the form of a rectangle,

$\therefore$ Perimeter of the rectangle $=104$ cm

$⟹2(y+y-4)=104$

$2y-4=52$

$⟹y-2=26$

$⟹y=28$

Area of rectangle $=28(28-4)=672c{m}^2$