Difference between revisions of "2007 Cyprus MO/Lyceum/Problem 7"
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Using <math>30-60-90</math> [[right triangle]] [[ratio]]s, the lengths of the sides of the rectangle are <math>\frac{d}{2}</math> and <math>\frac{d\sqrt{3}}{2}</math>. | Using <math>30-60-90</math> [[right triangle]] [[ratio]]s, the lengths of the sides of the rectangle are <math>\frac{d}{2}</math> and <math>\frac{d\sqrt{3}}{2}</math>. | ||
− | The area of the rectangle is <math>\frac{d^2\sqrt{3}}{4}\ | + | The area of the rectangle is <math>\frac{d^2\sqrt{3}}{4}\Longrightarrow\mathrm{ A}</math>. |
==See also== | ==See also== |
Latest revision as of 20:43, 6 May 2007
Problem
If a diagonal of a rectangle forms a
angle with one of its sides, then the area of the rectangle is
Solution
Using right triangle ratios, the lengths of the sides of the rectangle are
and
.
The area of the rectangle is .
See also
2007 Cyprus MO, Lyceum (Problems) | ||
Preceded by Problem 6 |
Followed by Problem 8 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 |