area = s(2s)sin45° = 8/√2
2s^2(1/√2) = 8/√2
2s^2 = 4
take over
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.
7 answers
I inputted √2 into my thing, and it said wrong.
Answer:
2 sqrt(2)
2 sqrt(2)
loser wrong the anser is 7*sqrt2 this is how I did it:
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no the answer is 2sqrt(2)
you
are
wrong
also jiskha is not a loser
maybe you are
you
are
wrong
also jiskha is not a loser
maybe you are
ya its 2sqrt2
If we let the side of length 2s be the base of the parallelogram, we can use our 45-degree angle to find the height of the parallelogram. The height and sides of the parallelogram form a 45-45-90 triangle, with the side of length s as the hypotenuse. Thus, the height of the parallelogram is s/sqrt2.
It follows that the area of the parallelogram is $2s\cdot (s/\sqrt{2}) = s^2\sqrt{2} = 8\sqrt{2}$, so $s^2 = 8$. Taking the square root of both sides, we see that s=2sqrt2 - AOPS answers dont post aops on these sites plz
If we let the side of length 2s be the base of the parallelogram, we can use our 45-degree angle to find the height of the parallelogram. The height and sides of the parallelogram form a 45-45-90 triangle, with the side of length s as the hypotenuse. Thus, the height of the parallelogram is s/sqrt2.
It follows that the area of the parallelogram is $2s\cdot (s/\sqrt{2}) = s^2\sqrt{2} = 8\sqrt{2}$, so $s^2 = 8$. Taking the square root of both sides, we see that s=2sqrt2 - AOPS answers dont post aops on these sites plz
Just submit "2sqrt2" that will do the trick
3 answers