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 $\frac{1}{3}$ the first side of the rectangle. What is the area of the remaining portion?

• A. $\frac{3}{4}{x}^2$
• B. $\frac{7}{8}{x}^2$
• C. $\frac{11}{12}{x}^2$
• D. $\frac{15}{16}{x}^2$

Answer 1

The correct option is C $\frac{11}{12}{x}^2$

Each side of the square = x m
$\Rightarrow$ Area of the rectangle =$\frac{x}{2}m$ and
Other side of the square = $\frac{1}{3}\times \frac{x}{2}m=\frac{x}{6}m$
$\therefore$ Area of the rectangle = $\frac{x}{2}m\times \frac{x}{6}m$
$=\frac{x^2}{12}{m}^2$
$=\frac{11x^2}{12}{m}^2$