To find the area of a rectangle, you can use the formula:
\[ \text{Area} = \text{length} \times \text{width} \]
In Bianca's case, the beach towel has dimensions of 16 feet by 28 feet. Therefore, the area can be calculated as follows:
\[ \text{Area} = 16 \times 28 \]
Now, we can also explore the difference of squares. The identity for the difference of two squares is:
\[ a^2 - b^2 = (a - b)(a + b) \]
To express the area of the towel using the difference of squares, we can consider the dimension pairs and check which option can represent the area correctly.
To explore the dimensions 28 and 16, we can express:
\[ (28)^2 - (16)^2 = (28 - 16)(28 + 16) = 12 \times 44 \]
Calculating this gives:
\[ 12 \times 44 = 528 \]
Since the area of the beach towel is indeed:
\[ 16 \times 28 = 448 \]
So let's find the difference of squares correctly.
Now let's verify which one of the choices matches our findings in terms of giving us the area using the values:
- Option a: \(22^2 - 6^2\) = \(484 - 36 = 448\) (This could be a representation.)
- Option b: \(28^2 - 16^2\) = \(784 - 256 = 528\) (Doesn’t match.)
- Option c: \(28^2 - 6^2\) = \(784 - 36 = 748\) (Doesn’t match.)
- Option d: \(22^2 - 16^2\) = \(484 - 256 = 228\) (Doesn’t match.)
From these calculations, option a (22^2 - 6^2 = 448) is the option that uses the difference of squares to equal the area of the beach towel.
So, Bianca can use:
a. 22^2 - 6^2 to find the area of the beach towel.
2 answers