Math / Geometry

Question4. The ratio of the corresponding side lengths of two similar rectangular tables is $4: 5$ . a. What is the ratio of the perimeters? b. What is the ratio of the areas? c. The perimeter of the larger table is 44 feet. What is the perimeter of the smaller table?

Studdy Solution

STEP 1

1. The two tables are similar rectangles.
2. The ratio of the corresponding side lengths is $4:5$ .
3. The perimeter of the larger table is $44$ feet.

STEP 2

1. Determine the ratio of the perimeters.
2. Determine the ratio of the areas.
3. Calculate the perimeter of the smaller table.

STEP 3

The ratio of the perimeters of two similar figures is the same as the ratio of their corresponding side lengths. Therefore, the ratio of the perimeters is:
$4:5$

STEP 4

The ratio of the areas of two similar figures is the square of the ratio of their corresponding side lengths. Therefore, the ratio of the areas is:
$(4:5)^2 = 16:25$

STEP 5

To find the perimeter of the smaller table, use the ratio of the perimeters:
Let $P_s$ be the perimeter of the smaller table. Then:
$\frac{P_s}{44} = \frac{4}{5}$
Solve for $P_s$ :
$P_s = \frac{4}{5} \times 44$
$P_s = \frac{176}{5}$
$P_s = 35.2 \text{ feet}$
The solutions are: a. The ratio of the perimeters is $4:5$ . b. The ratio of the areas is $16:25$ . c. The perimeter of the smaller table is $35.2 \text{ feet}$ .

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