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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
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B
"k" cm, "y" cm
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C
"3k" cm, "y" cm
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D
"k" cm, "3y" cm
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Solution

The correct option is B "k" cm, "y" cm
Area of the square with side length "k" cm=k2 sq.cm

Area of the square with side length "y" cm=y2 sq.cm

Area of the square with side length "(k + y)" cm=(k+y)2 sq.cm

Total area of 2 rectangles=(k+y)2(k2+y2)

Now, expanding (k+y)2=(k+y)(k+y)

(k+y)2=k2+2ky+y2

(k+y)2(k2+y2) =k2+2ky+y2(k2+y2) =2ky

The two rectangles are identical. Hence, the area of each rectangle is ky sq.cm

,The dimesions of each rectangle are:
"k" cm, "y" cm

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