Question

A square of side x is taken. A rectangle is cut out from this square such that one side of the rectangle is half that of the square and the other is \(\frac13\) the first side of the rectangle. What is the area of the remaining portion?

(a) \(\frac34x^2\) 

(b) \(\frac78x^2\) 

(c) \(\frac{11}{12}x^2\) 

(d) \(\frac{15}{16}x^2\)

Answer 1

(c)  \( \frac{11x^2}{12}\) m²

Each side of the square = x m 

⇒ Area of the square = x² m² 

Given, one side of the rectangle = \(\frac{x}2\) m and other side of the square = \(\frac13\) x \(\frac{x}2\) m = \(\frac{x}2\) m

∴ Area of the rectangle = \(\frac{x}2\) m x \(\frac{x}2\) m = \(\frac{x^2}{12}\) m²

∴ Area of the remaining portion = \(x^2-\frac{x^2}{12} = \frac{11x^2}{12}\) m²