By what factor should we multiply the ratio 60 : 40 (image A) to get 90 : 60 (image D)?

Question

Homi · Accepted Answer

We need to find a number that multiplies the width and height of Image A to get the width and height of Image D.

Step 1 — Identify the Ratios

First, let us write down the dimensions for Image A and Image D. The dimensions for Image A are 60 mm (width) and 40 mm (height). The dimensions for Image D are 90 mm (width) and 60 mm (height).

Step 2 — Calculate the Width Factor

To find the factor for the width, we divide the width of Image D by the width of Image A. Let the width factor be $F_w$ .

$F_w = \frac{\text{Width of Image D}}{\text{Width of Image A}}$

$F_w = \frac{90 \text{ mm}}{60 \text{ mm}}$

$F_w = \frac{9}{6}$

$\boxed{F_w = \frac{3}{2}}$

Diagram 1

Step 3 — Calculate the Height Factor

Similarly, to find the factor for the height, we divide the height of Image D by the height of Image A. Let the height factor be $F_h$ .

$F_h = \frac{\text{Height of Image D}}{\text{Height of Image A}}$

$F_h = \frac{60 \text{ mm}}{40 \text{ mm}}$

$F_h = \frac{6}{4}$

$\boxed{F_h = \frac{3}{2}}$

Step 4 — State the Overall Factor

Both the width factor and the height factor are the same. This means Image D is a scaled version of Image A. The factor by which we should multiply the ratio 60 : 40 is $\frac{3}{2}$ . We can also write this as a decimal.

$\frac{3}{2} = 1.5$

$\boxed{\text{Factor} = \frac{3}{2} \text{ or } 1.5}$

Answer

The factor is $\frac{3}{2}$ (which is 1.5).

Question 3

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