Question

I can certainly help with specific questions or problems, but I need you to provide the specific question or topic you'd like assistance with. Please provide the information you need help with.

Answer 1

The area of the original square is 49 square meters.

Step-by-step explanation:

Let's denote the side length of the original square as (a). The area of the square is given by
`\(A = a^2\)`. When two opposite sides are increased by 10 meters, the new length becomes (a + 10), and when the other two sides are decreased by 8 meters, the new length becomes (a - 8). This forms a rectangle, and the area of the rectangle is given by
`\(A_{\text{rectangle}} = (a + 10)(a - 8)\)`.

According to the problem, the area of the rectangle is 63 square meters:

(a + 10)(a - 8) = 63

Expanding and simplifying:

`\[ a^2 + 2a - 80 = 63 \]`

Subtracting 63 from both sides:

`\[ a^2 + 2a - 143 = 0 \]`

Now, we can factor this quadratic equation:

(a - 11)(a + 13) = 0

This gives us two possible solutions for (a): (a = 11) or (a = -13). Since the side length cannot be negative, we discard (a = -13).

Therefore, the side length of the original square is (a = 11), and the area of the square is:

`\[ A = a^2 = 11^2 = 121 \]`

So, the area of the original square is 121 square meters.

Complete Question:

If two opposite sides of a square are increased by 10 meters and the other sides are decreased by 8 meters, the area of the rectangle that is formed is 63 square meters. Find the area of the original square.