Question

A rectangular piece of dimension 3 cm × 2 cm was cut from a rectangular sheet of

paper of dimensions 6 cm × 5 cm. Find the ratio of the areas of the two rectangles.​

Answer 1

Given: Length of the small rectangular piece = 3cm

Width of the small rectangular piece = 2cm

Length of the large rectangular piece = 6cm

Width of the large rectangular piece = 5cm

The small piece was cut out from the large rectangle

To Find: Ratio of areas of the two rectangular pieces

Solution:

Area of the rectangle is given as

Area = Length x width

Area of the small rectangle = Length of the small rectangle x width of the small rectangle

Area of the small rectangle =  3 x 2

                                             = 6 cm²

Area of the large rectangle = Length of the large rectangle x width of the large rectangle

Area of the large rectangle = 6 x 5

                                              = 30 cm²

The smaller rectangle is cut out from the larger piece, so the area of the remaining piece will be

Area of remaining piece = Area of the large rectangle - Area of the small rectangle

Area of remaining piece =  30 - 6

                                        = 24 cm²

Area of the small rectangle/area of the remaining piece = 6 / 24

                                                                                              = 1 / 4

Therefore, the required ratio is 1:4.