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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.

 Apr 10, 2019

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 \(\frac{s\sqrt{2}}{2}*2s=8\sqrt{2}, 2s^2=16, s^2=8, s=2\sqrt2.\) 

 Apr 10, 2019

Sorry, tertre....didn't know that was you answering....good job!!!!


cool cool  cool

CPhill  Apr 10, 2019

Thank you...it's my fault, could have been logged in ...!

tertre  Apr 10, 2019

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




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



cool cool cool

 Apr 10, 2019

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