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

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

1. Let’s denote the length of the shorter side of the parallelogram through x.

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

4 * x = 4x.

3. Let’s 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 length of the shorter side of the parallelogram is x = 2√2.

5. What is the length of the longer 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) = (32/2) * √2 = 16√2.

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