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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
 #1
avatar+4247 
+3

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
 #3
avatar+101084 
+1

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

 

cool cool  cool

CPhill  Apr 10, 2019
 #4
avatar+4247 
+2

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

tertre  Apr 10, 2019
 #2
avatar+101084 
+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

 

 

cool cool cool

 Apr 10, 2019

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