Question

show what you know
aaliyah is making a scale drawing of a rectangular swimming pool. the pool is 50 meters long and 25 meters wide. she originally used a scale of 1 centimeter to 10 meters for her drawing of the pool.
a aaliyah needs her drawing to be larger. suggest a new scale for aaliyah.
b determine the side lengths of the scale drawing using the new scale.
show what you know
here are two scale drawings of the hagia sophia in istanbul, turkey.
what is the unknown value in the scale?
explain your thinking.

Explanation:

Step1: Suggest a new scale

To make the drawing larger, we can use a scale with a smaller denominator for the ratio. A new scale of 1 centimeter to 5 meters can be used.

Step2: Calculate the length of the scale - drawing for the pool

The actual length of the pool is 50 meters. Using the new scale of 1 cm to 5 m, the length on the scale - drawing $l=\frac{50}{5}=10$ cm.

Step3: Calculate the width of the scale - drawing for the pool

The actual width of the pool is 25 meters. Using the new scale of 1 cm to 5 m, the width on the scale - drawing $w = \frac{25}{5}=5$ cm.

For the second part about the Hagia Sophia scale - drawings:
Let's assume the two scale - drawings are similar. If we count the number of grid squares for the known and unknown lengths in the two drawings and set up a proportion. Suppose the number of grid squares for the known length of 10 m is $n_1$ and for the unknown length is $n_2$. If the scale is consistent between the two drawings, we can set up the proportion $\frac{10}{n_1}=\frac{x}{n_2}$, where $x$ is the unknown length. However, since no information about the grid - square count is given in the problem description (assuming we need to use the grid - square method), if we assume a simple visual proportion and assume the two drawings are in a simple ratio. If the first drawing is a reduced version of the second, we need more information like the ratio of the sizes of the two drawings in terms of grid - squares or some other reference. But if we assume the first drawing is half the size of the second in terms of linear dimensions, the unknown value could be 20 m.

Answer:

a. New scale: 1 centimeter to 5 meters
b. Length of scale - drawing: 10 cm, Width of scale - drawing: 5 cm
For the Hagia Sophia problem, assuming simple visual proportion and the first drawing is half the size of the second in linear dimensions, the unknown value is 20 m.