Question

A small rectangular piece of length $\frac{5}{12}$ ft and width $\frac{4}{17}$ ft is cut out from a cardboard sheet of area $\frac{3}{17}$ sq ft as shown in the figure below.

Find the remaining area of the cardboard sheet.

• A. 2/51 sq ft
• B. 3/34 sq ft
• C. 1/17 sq ft
• D. 4/51 sq ft

Answer 1

The correct option is D 4/51 sq ft

Initial area of the carboard sheet
= $\frac{3}{17}$ sq ft
Area of the small rectangular piece
= Length × Width
= $\frac{5}{12}$ × $\frac{4}{17}$
= $\frac{5}{51}$ sq ft

Remaining area of the cardboard sheet = Initial area of the cardboard sheet - Area of the small rectangular piece
= $\frac{3}{17}$ - [ $\frac{5}{12}$ × $\frac{4}{17}$ ]
=$\frac{3}{17}$ - $\frac{5}{51}$
= $\frac{9-5}{51}$
= $\frac{4}{51}$ sq ft
Therefore, the remaining area of the cardboard sheet is $\frac{4}{51}$ sq ft.