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# help

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

CPhill  Apr 10, 2019
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Thank you...it's my fault, could have been logged in ...!

tertre  Apr 10, 2019
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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

Apr 10, 2019