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=k2sq.cm
Area of the square with side length "y" cm=y2sq.cm
Area of the square with side length "(k + y)" cm=(k+y)2sq.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 kysq.cm
∴,The dimesions of each rectangle are:
"k" cm, "y" cm