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(a) On this grid, draw the path around the square of side 3. [1]
(b) On this grid, draw the path around a square of side 4. [1]
(c) This table shows the number of tiles in the paths around squares of different sizes. Complete the table.
[Table_1]
| Side of square | Number of tiles in path |
|---|---|
| 1 | 8 |
| 2 | |
| 3 | |
| 4 |
[1]
(d) Work out the number of tiles that make the path around a square of side 6. [2]
..................................................................................................(e) Explain why the path around a square cannot have exactly 50 tiles. [1]
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(f) Find an expression, in terms of $n$, for the number of tiles in the path around a square of side $n$. [2]
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(g) Work out the number of tiles in the path around a square of side 88. [2]
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(h) The path around a square has 400 tiles. Work out the area of the square. [3]
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546
527
535
(a) On the grid, draw a diagram to show the path around the given rectangles.
Rectangle width 1 and length 3 & Rectangle width 1 and length 4
(b) Complete the table to show the number of tiles in the paths around rectangles of width 1 with different lengths.
[Table_1]
(c) Find an expression, in terms of $L$, for the number of tiles in the path around a rectangle of width 1 and length $L$.
585
511
523
(a) (i) Complete the table to show the number of tiles in the paths around rectangles of width 2 with different lengths. You may use the grid to help you.
[Table]
$$\begin{array}{|c|c|}\hline \text{Length of rectangle (L)} & \text{Number of tiles in path} \\ \hline 1 & \\ \hline 2 & \\ \hline 3 & \\ \hline 4 & \\ \hline \end{array}$$
(a) (ii) Find an expression, in terms of $L$, for the number of tiles in the path around a rectangle of width 2 and length $L$.
(b) Find an expression, in terms of $L$, for the number of tiles in the path around a rectangle of width 3 and length $L$.
(c) Complete the table. Use your expressions from Questions 2(c), 3(a)(ii) and 3(b).
[Table]
$$\begin{array}{|c|c|}\hline \text{Width of rectangle (W)} & \text{Number of tiles in path around a rectangle of length L} \\ \hline 1 & \\ \hline 2 & \\ \hline 3 & \\ \hline 4 & \\ \hline \end{array}$$
(d) Find an expression, in terms of $L$ and $W$, for the number of tiles in the path around a rectangle of length $L$ and width $W$.
(e) Use your answer to part (d) to write an expression for the number of tiles in the path around a rectangle of length $n$ and width $n$. Give your answer in its simplest form.
594
587
558
The path around a rectangle has 20 tiles.
Complete the table to show all the possible lengths and widths of the rectangle.
You may not need all the rows.
You may use the grid to help you.
[Table_1]
$$\begin{array}{|c|c|} \hline \text{Length of rectangle (L)} & \text{Width of rectangle (W)} \\ \hline \\ \hline \\ \hline \\ \hline \\ \hline \\ \hline \end{array}$$
[Grid_1]
529
592
560
