1. Seamstress Ana has a piece of fabric in the shape of a rectangle where the length of one side is $70 \%$ of the length of the other side. By cutting the fabric along the line whose endpoints are the midpoints of two adjacent sides of the rectangle, she obtained pieces in the shape of a right triangle and a pentagon. The perimeter of the pentagon is $68 \mathrm{dm}$ greater than the perimeter of the triangle. What is the area of the fabric?
First method:

Let $a$ and $b$ be the lengths of two adjacent sides of a rectangle, and $a > b$. Let $x$ be the length of the line segment whose endpoints are the midpoints of the adjacent sides of the rectangle.

We have $b = 70\% \cdot a = 0.7 \cdot a$.

$\boldsymbol{a}$

![](https://cdn.mathpix.com/cropped/2024_05_30_ba00de53bdad84e80dffg-01.jpg?height=346&width=740&top_left_y=1186&top_left_x=635)

$a + 0.7a + 0.5a + x + 0.35a = 0.5a + 0.35a + x + 68$

$2.55a + x = 0.85a + x + 68$

$2.55a = 0.85a + 68$

$2.55a - 0.85a = 68$

$1.7a = 68$

$a = 68 : 1.7$

$a = 40 \text{ dm}$

$b = 0.7 \cdot a$

$b = 0.7 \cdot 40$

$b = 28 \text{ dm}$

The area of the canvas is $(40 \cdot 28) \text{ dm}^2 = 1120 \text{ dm}^2$.