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03 Dec 2018, 07:24
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E
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Difficulty:
15%
(low)
Question Stats:
83% (01:39) correct
17%
(02:06)
wrong
based on 514
sessions
History
Date
Time
Result
Not Attempted Yet
In the figure above, square CDEF has area 4. What is the area of △ ABF?
(A) 2\(\sqrt{2}\)
(B) 2\(\sqrt{3}\)
(C) 4
(D) 3\(\sqrt{3}\)
(E) 6
Attachment:
ABF.JPG [ 19.41 KiB | Viewed 9533 times ]
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03 Dec 2018, 10:48
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IMO E
Triangle \(CFB\) is a 30-60-90 triangle, therefore is side \(FB=2*\sqrt{3}\)...
Triangle \(ABF\) is a 45-45-90 triangle (isosceles right triangle), therefore is side \(BF=AB\) and the hypotenuse is equal to \(2*\sqrt{3}*\sqrt{2}\)
Area of \(ABF=\) \(\frac{1}{2}*2*\sqrt{3}*2*\sqrt{3}=\)\(6\)
Triangle \(CFB\) is a 30-60-90 triangle, therefore is side \(FB=2*\sqrt{3}\)...
Triangle \(ABF\) is a 45-45-90 triangle (isosceles right triangle), therefore is side \(BF=AB\) and the hypotenuse is equal to \(2*\sqrt{3}*\sqrt{2}\)
Area of \(ABF=\) \(\frac{1}{2}*2*\sqrt{3}*2*\sqrt{3}=\)\(6\)
Attachments
Screen Shot 2018-12-03 at 18.36.52.png [ 134.78 KiB | Viewed 9080 times ]
General Discussion
17 Jan 2019, 12:33
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HKD1710
If the area of the square is 4, then each side has length 2
At this point, we have a special 30-60-90 right triangle. When we compare this blue triangle to the BASE 30-60-90 right triangle . . .
. . . we see that the blue triangle TWICE the size of the BASE 30-60-90 right triangle
So, These are the measurements of the blue triangle
Finally, we have special 45-45-90 right triangle.
This triangle is also an ISOSCELES triangle, so the other side ALSO has length 2√3
What is the area of △ABF?
area of a triangle = (base)(height)/2
So, area of △ABF = (2√3)(2√3)/2
= (4√9)/2
= (4)(3)/2
= 12/2
= 6
Answer: E
Cheers,
Brent
