Question

Two squares, one of side length "k" cm and the other of side length "y" cm, are combined with two identical rectangles to form a new square. If the side length of the new square is "y + k" cm, what could be the dimensions of the rectangles?

• A. "k" cm, "2y" cm
• B. "k" cm, "y" cm
• C. "3k" cm, "y" cm
• D. "k" cm, "3y" cm

Answer 1

The correct option is B "k" cm, "y" cm

$\text{Area of the square with side length "k" cm}=k^{2}sq.cm$

$\text{Area of the square with side length "y" cm}=y^{2}sq.cm$

$\text{Area of the square with side length "(k + y)" cm}=(k+y{)}^{2}sq.cm$

$\therefore \text{Total area of 2 rectangles}=(k+y{)}^2-(k^2+y^2)$

$\text{Now, expanding}$ $(k+y{)}^2=(k+y\left)\right(k+y)$

$(k+y{)}^2=k^2+2ky+y^2$

$⟹(k+y{)}^2-(k^2+y^2)=k^2+2ky+y^2-(k^2+y^2)=2ky$

$\text{The two rectangles are identical. Hence, the}\text{area of each rectangle is}kysq.cm$

$\therefore ,\text{The dimesions of each rectangle are:}$
"k" cm, "y" cm