Question

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

Answer 1

The total length of the aluminum strip = $\text{40 cm.}$

“If we are preparing a rectangular frame from this aluminum strip then the perimeter of the rectangular frame will be equal to the total length of the aluminum strip”.

The perimeter of the rectangular frame = $\text{40 cm.}$

$\text{2×}\left(\text{l+b}\right)\text{= 40 cm}$

$\text{l+b = 20 cm}$

The length and breadth of the rectangular frame will be all integral values whose sum is $20.$

So, the possible measurements can be -

$$\begin{gathered} \left(\text{1 cm, 19 cm}\right),\left(\text{2 cm, 18 cm}\right),\left(\text{3 cm, 17 cm}\right),\left(4\text{cm, 16 cm),}\right(5\text{cm, 15 cm)} \\ \left(6\text{cm, 14 cm),}\right(7\text{cm, 13 cm),}\left(8\text{cm, 12 cm),}\right(9\text{cm, 11 cm),}(10\text{cm, 10 cm)} \end{gathered}$$

Hence, above are the possible measurements that can be used to prepare the rectangular frame.