Question

Consider this scaled figure of a swimming pool. The dimensions of the original pool are 24 feet wide by 36 feet long. A rectangle has a width of 6. 4 feet and width of question mark feet. Use the measurements of the original and of the scaled figure to find the scale factor and the missing length. What is the scale factor? What is the missing length of the scale model?.

Answer 1

The scale factor used for scaling the actual rectangular pool was 4/15 and the length of the scaled rectangle is 9.6 feet.

How to calculate the scale factor?

Suppose the initial measurement of a figure was x units.

And let the figure is scaled and new measurement is of y units.

Since the scaling is done by multiplication of some constant, that constant is called scale factor. Let that constant be 's'.

Then we have:

$s \times x = y\\s = \dfrac{y}{x}$

Thus, scale factor is the ratio of the new measurement to the old measurement.

For this case, we're specified that:

Dimensions of the original pool = 24 feet wide by 36 feet long

The scaled rectangle's dimension: 6.4 feet width and L feet length (we assume the length be L units).

So, in scale drawing, 24 feet was converted to 6.4 feet. Let the scale factor be 's', then:

$6.4 = s \times 24\\\\s = \dfrac{6.4}{24} = \dfrac{4}{15}$

Thus, since length is also scaled by same factor(as the whole figure is scaled by constant scale factor assumingly), we get:

Scaled length = s times original length

$L = \dfrac{4}{15} \times 36 = 9.6 \: \rm feet$

Thus, the scale factor used for scaling the actual rectangular pool was 4/15 and the length of the scaled rectangle is 9.6 feet.

Learn more about scale factors here :

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