2005 AMC 10A Problems/Problem 4: Difference between revisions
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==Solution== | ==Solution 1== | ||
Let's set our length to <math>2</math> and our width to <math>1</math>. | Let's set our length to <math>2</math> and our width to <math>1</math>. | ||
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-JinhoK | -JinhoK | ||
==Solution 2== | |||
Call the length <math>2l</math> and the width <math>l</math>. | |||
We have our area as <math>2*1 = 2</math> and our diagonal: <math>x</math> as <math>\sqrt{1^2+2^2} = \sqrt{5}</math> (Pythagoras Theorem) | |||
Now we can plug this value into the answer choices and test which one will give our desired area of <math>2</math>. | |||
* All of the answer choices have our <math>x</math> value squared, so keep in mind that <math>\sqrt{5}^2 = 5</math> | |||
Through testing, we see that <math>{2/5}*\sqrt{5}^2 = 2</math> | |||
So our correct answer choice is <math>\mathrm{(B) \ } \frac{2}{5}x^2\qquad</math> | |||
-mobius247 | |||
==See also== | ==See also== | ||
Revision as of 13:04, 31 May 2021
Problem
A rectangle with a diagonal of length 
and the length is twice as long as the width. What is the area of the rectangle?
Video Solution
CHECK OUT Video Solution: https://youtu.be/X8QyT5RR-_M
Solution 1
Let's set our length to 
and our width to 
.
We have our area as 
and our diagonal: as 
(Pythagoras Theorem)
Now we can plug this value into the answer choices and test which one will give our desired area of .
- All of the answer choices have our
value squared, so keep in mind that 
Through testing, we see that 
So our correct answer choice is 
-JinhoK
Solution 2
Call the length 
and the width 
.
We have our area as and our diagonal: as (Pythagoras Theorem)
Now we can plug this value into the answer choices and test which one will give our desired area of .
- All of the answer choices have our value squared, so keep in mind that
Through testing, we see that
So our correct answer choice is
-mobius247
See also
| 2005 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 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 | ||
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