Question

On the occasion of Republic day, a school organized a poster making competition for the students of class-VI. The topic was “National Integration”. Each child was given a square sheet of side 60 cm. They had to make a border of width 2 cm using the coloured tape and the remaining portion had to be divided into four equal portions to show the main teachings of different religions.
(a) Find the length of the coloured tape needed to border?
(b) What will be the side of the square into which the sheet has been divided?

Answer 1

Hint: We start solving the problem by assigning variables to the vertices of the given square sheet. We then draw all the given information to get a better view. We can then see that the coloured tape covers all the sides of the given square sheet which will be equal to the sum of the lengths of all sides of that square. We can then see that each side of the square sheet is reduced by 2cm to get the required square which has been divided.

Complete step-by-step answer:
According to the problem, we have a square sheet of side 60 cm. A border has to be made using the coloured tape of width 2 cm and the remaining portion is divided into four equal portions.
Let us assume ABCD be the square sheets and \[{{A}_{1}}{{B}_{1}}{{C}_{1}}{{D}_{1}}\] be the remaining portion that is divided into four equal portions. Let us draw this information to get a better view.

(a) Now, we need to find the length of the coloured tape used to border the square sheet.
From the figure we can see that the length of the border is equal to the sum of the lengths of all sides of square ABCD.
So, we have a length of coloured tape = $60cm+60cm+60cm+60cm$.
length of coloured tape = $240cm$.
∴ The length of the coloured tape used to border is 240 cm.
(b) Now, we need to length of the side of square \[{{A}_{1}}{{B}_{1}}{{C}_{1}}{{D}_{1}}\] after bordering the square sheet ABCD.
From the figure, we can see that the length of each side of square sheet ABCD is reduced by 2cm to become the square \[{{A}_{1}}{{B}_{1}}{{C}_{1}}{{D}_{1}}\].
So, the length of the side of square \[{{A}_{1}}{{B}_{1}}{{C}_{1}}{{D}_{1}}\] = $\left( 60-2 \right)$cm.
Length of the side of square \[{{A}_{1}}{{B}_{1}}{{C}_{1}}{{D}_{1}}\] = 58cm.
∴ The length of the square \[{{A}_{1}}{{B}_{1}}{{C}_{1}}{{D}_{1}}\] is 58cm.

Note: We can see that the length of the coloured tape is equal to the perimeter of the square which is 4 times the length of the side of the square. We can also find the area of the square sheet and the finally obtained square after bordering it. We can also find the area of the tape that is used for bordering the square sheet. Similarly, we can expect the problems to find the area divided to write about different religions.