A parallelogram has adjacent sides of lengths s units and 2s units forming a 45-degree angle. The area of the parallelogram is \(8\sqrt 2\) square units. What is the value of s? Express your answer in simplest radical form.

Logic Apr 10, 2019

#1**+2 **

Draw a parallelogram.

Break the parallelogram into two 45-45-90 triangles.

Take one of the triangles, and fill in all the missing lengths.

Opposite to the 45 angles should be \(\frac{s\sqrt{2}}{2}\).

Now, the area of a a parallelogram is base * height, and \(\frac{s\sqrt{2}}{2}*2s=8\sqrt{2}, 2s^2=16, s^2=8, s=2\sqrt2.\)

tertre Apr 10, 2019

#2**+2 **

If we draw a diagonal....this will divide the parallelogram into two equal areas

So....one of these areas forms a triangle with an area of 4√2 and sides of s and 2s and an included angle between these sides of 45 degrees

So

Area of triangle = (1/2 (s) (2s)sin (45)

4√2 = (1/2)(2s^2) * (1/√2)

4√2 = s^2/ √2 multiply both sides by √2

4√2 *√2 = s^2

4 * 2 = s^2

2 √2 = s

CPhill Apr 10, 2019