Difference between revisions of "1978 AHSME Problems/Problem 25"
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==Problem== | ==Problem== | ||
| − | Let <math> | + | Let <math>a</math> be a positive number. Consider the set <math>S</math> of all points whose rectangular coordinates <math>(x, y )</math> satisfy all of the following conditions: |
<math>\text{(i) }\frac{a}{2}\le x\le 2a\qquad \text{(ii) }\frac{a}{2}\le y\le 2a\qquad \text{(iii) }x+y\ge a\\ \\ \qquad \text{(iv) }x+a\ge y\qquad \text{(v) }y+a\ge x</math> | <math>\text{(i) }\frac{a}{2}\le x\le 2a\qquad \text{(ii) }\frac{a}{2}\le y\le 2a\qquad \text{(iii) }x+y\ge a\\ \\ \qquad \text{(iv) }x+a\ge y\qquad \text{(v) }y+a\ge x</math> | ||
| − | The boundary of set S is a polygon with | + | The boundary of set <math>S</math> is a polygon with |
<math>\textbf{(A) }3\text{ sides}\qquad \textbf{(B) }4\text{ sides}\qquad \textbf{(C) }5\text{ sides}\qquad \textbf{(D) }6\text{ sides}\qquad \textbf{(E) }7\text{ sides}</math> | <math>\textbf{(A) }3\text{ sides}\qquad \textbf{(B) }4\text{ sides}\qquad \textbf{(C) }5\text{ sides}\qquad \textbf{(D) }6\text{ sides}\qquad \textbf{(E) }7\text{ sides}</math> | ||
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==Solution== | ==Solution== | ||
| − | <math>\fbox{D}</math> | + | Draw a picture. The answer is <math>\fbox{D}</math>. |
Latest revision as of 17:31, 28 August 2023
Problem
Let 
be a positive number. Consider the set 
of all points whose rectangular coordinates 
satisfy all of the following conditions:
The boundary of set is a polygon with
Solution
Draw a picture. The answer is 
.
