Carcass wrote:
Attachment:
triangles.jpg
∠ ABC = 45 ° and ED = DF. The area of triangle ABC is 4 times the area of triangle DEF.
Quantity A |
Quantity B |
\(\frac{AC}{EF}\) |
\(\sqrt{2}\) |
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
In triangle ABC we have ∠ ABC = 45 ° , ∠ CAB = 90 °
Therefore ∠ ACB = 45 °
So the triangle is isosceles triangle
Similarly in triangle DEF, we have DF = DE and ∠ FDE = 90 °
Therefore ∠ DEF = ∠ DFE = 45 °
Now we can write as
\(\frac{1}{2} AC^2 = 4* \frac{1}{2} DF^2\)
or
\(AC = 2*DF\)In triangle DEF, since it is 90-45-45 the sides are distributed in
\(1 : 1 : \sqrt2\)
i.e. \(DF = DE = 1\) and \(EF = \sqrt2\)
Therefore AC = 2 * 1 = 2
Now \(QTY A =\frac{AC}{EF} = \frac{2}{{\sqrt2}}\) =\(2 *\frac{{\sqrt2}}{{\sqrt2 *\sqrt2}}\) = \(\sqrt2\)
Hence QTY A = QTY B
_________________
If you found this post useful, please let me know by pressing the Kudos ButtonRules for PostingGot 20 Kudos? You can get Free GRE Prep Club TestsGRE Prep Club Members of the Month:TOP 10 members of the month with highest kudos receive access to 3 months
GRE Prep Club tests