Two rectangles, Rectangle A and Rectangle B are in proportion in the ratio 3:5. If the area of Rectangle B is 80cm², find the area of Rectangle A

To solve this problem, we can use the concept of ratios and proportions.

Given:
- The ratio of the dimensions of Rectangle A to Rectangle B is \( 3:5 \).
- The area of Rectangle B is \( 80 \, \text{cm}^2 \).

Let's denote the area of Rectangle A as \( A_A \) and the area of Rectangle B as \( A_B = 80 \, \text{cm}^2 \).

Since the rectangles are similar and their dimensions are in the ratio \( 3:5 \), the ratio of their areas will be the square of the ratio of their corresponding sides. Thus, the ratio of the areas of Rectangle A to Rectangle B is:

\[
\left(\frac{3}{5}\right)^2 = \frac{9}{25}
\]

So, the area of Rectangle A to the area of Rectangle B can be expressed as:

\[
\frac{A_A}{A_B} = \frac{9}{25}
\]

Substituting the given area of Rectangle B:

\[
\frac{A_A}{80} = \frac{9}{25}
\]

Now, solve for \( A_A \):

\[
A_A = \frac{9}{25} \times 80 = \frac{720}{25} = 28.8 \, \text{cm}^2
\]

Thus, the area of Rectangle A is \( 28.8 \, \text{cm}^2 \).

Would you like more details or have any questions? Here are five related questions you might find interesting:

1. How would the solution change if the ratio was 4:5 instead of 3:5?
2. If the perimeter of Rectangle B is 36 cm, what is the perimeter of Rectangle A?
3. What is the ratio of the perimeters of Rectangle A to Rectangle B?
4. If Rectangle A has a width of 4 cm, what is its length?
5. How would the area of Rectangle A change if the ratio of their sides were squared?

**Tip:** When dealing with similar figures, remember that the ratio of their areas is the square of the ratio of their corresponding sides.

Learn how to find the area of Rectangle A when it is in proportion to Rectangle B in the ratio 3:5. Detailed step-by-step solution using ratios and proportions. Suitable for Grades 7-9.

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