Difference between revisions of "2002 AMC 10P Problems/Problem 6"
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== Problem == | == Problem == | ||
| − | The perimeter of a rectangle <math>100</math> and its diagonal has length <math>x.</math> What is the area of this rectangle? | + | The perimeter of a rectangle is <math>100</math> and its diagonal has length <math>x.</math> What is the area of this rectangle? |
<math> | <math> | ||
\text{(A) }625-x^2 | \text{(A) }625-x^2 | ||
Latest revision as of 19:29, 15 July 2024
Problem
The perimeter of a rectangle is 
and its diagonal has length 
What is the area of this rectangle?
Solution 1
Let 
be the length of the rectangle and 
be the width of the rectangle. We are given 
and 
We are asked to find the area, which is equivalent to 
Using a bit of algebraic manipulation:
Thus, our answer is 
See also
| 2002 AMC 10P (Problems • Answer Key • Resources) | ||
| Preceded by Problem 5 |
Followed by Problem 7 | |
| 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 | ||
| All AMC 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
