Question

The length of an aluminium strip is 40 cm. If the lengths in cm are measured in natural numbers, write the measurement of all the possible rectangular frames which can be made out of it. (For example, a rectangular frame with 15 cm length and 5 cm breadth can be made from this strip.)

Answer 1

Given, length of an aluminium strip = 40 cm

If this aluminium strip is used to make rectangular frame, then

Perimeter of rectangular frame = 40 cm

⇒ 2(x + y) = 40 cm   ...[Assuming x and y as the length and breadth of rectangular frame, respectively]

⇒ `(2(x + y))/2 = 40/2`   ...[Dividing both sides by 2]

⇒ x + y = 20 cm

Now, if the value of both length and breadth are natural numbers, then possible dimensions are as follows

Dimensions (in cm): 1 × 19, 2 × 18, 3 × 17, 4 × 16, 5 × 15, 6 × 14, 7 × 13, 8 × 12, 9 × 11, 10 × 10