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In the diagrams below, rectangle B is an enlargement of rectangle A.
(a)
Write down the scale factor of this enlargement.
................................................
(b)
Write down the scale factor of this enlargement.
................................................
(c)
For this pair of rectangles, the scale factor is 10.
Work out the length of rectangle B.
................................................
(d)
Work out the length of rectangle B.
................................................
528
570
524
(a) The diagram shows a 3 by 10 rectangle.
This is a scale-rectangle.
Show that it has a factor of 3.
(b) The diagram shows a 2 by 4 rectangle.
Is this a scale-rectangle?
Write Yes or No and give reasons for your answer.
(c) The diagram shows a scale-rectangle with a factor of 7.
(i) Find $m$. .........................................................
(ii) Write down the dimensions of the scale-rectangle. ....................... by ......................
(d) The diagram shows a scale-rectangle with a factor of 5.
(i) Find $w$. .........................................................
(ii) Write down the dimensions of the scale-rectangle. ....................... by ......................
507
532
566
The diagram shows a \textit{scale-rectangle} with a factor of $n$.
(a) When $x = 2$ and $n = 6$, (i) work out $y$, ..........................................................
(ii) find $z$, ..........................................................
(iii) complete this statement with a number, $$z = \ldots\ldots\ldots\ldots\ldots\ldots \times x$$
(iv) write down the connection between your answer to \textit{part (iii)} and the factor, $n$.
(b) When $x = 2$ and $z = 18$, (i) find $n$, ..........................................................
(ii) work out the dimensions of this \textit{scale-rectangle}.
.......................... by ..........................
(c) Use your answers to \textit{part (a)} and \textit{part (b)} to complete the second and third rows of the table. Complete the remaining rows of the table.
[Table_1]
$$\begin{array}{ccccc}
n & x & y & z & \text{Dimensions} \\
2 & 2 & 4 & 8 & 4 \text{ by } 10 \\
6 & 2 & & & \ldots\ldots \text{ by } \ldots\ldots \\
& 2 & & 18 & \ldots\ldots \text{ by } \ldots\ldots \\
5 & 7 & & & \ldots\ldots \text{ by } \ldots\ldots \\
1 & 4 & 16 & 4 & 4 \text{ by } 17 \\
5 & 20 & & & \ldots\ldots \text{ by } \ldots\ldots \\
\end{array}$$
529
537
550
The diagram shows a scale-rectangle with a factor of $n$.
(a) Work out the dimensions of this scale-rectangle in terms of $n$ and $x$.
.................... by ....................
(b) Show that, for any scale-rectangle, its dimensions are in the ratio
width : length $= n : n^2 + 1$.
563
569
536
