One side of a parallelogram is 4 times the other. Find the area of a parallelogram if its perimeter

One side of a parallelogram is 4 times the other. Find the area of a parallelogram if its perimeter is 20√2 and its acute angle is 45 degrees.

1. Let’s denote the smaller side of the parallelogram by x.

2. Determine the length of the longer side of the parallelogram

4 * x = 4x.

3. Since the perimeter of the parallelogram is 20√2, compose and solve the equation:

(x + 4x) * 2 = 20√2;

5x = 20√2: 2;

5x = 10√2;

x = 10√2: 5;

x = 2√2.

4. The smaller side of the parallelogram is 2√2.

5. What is the large side of the parallelogram?

4 * 2√2 = 8√2.

6. What is the area of the parallelogram?

2√2 * 8√2 * sin450 = 32 * (√2 / 2) = 16√2.

Answer: the area of the parallelogram is 16√2.