Difference between revisions of "2003 AMC 10B Problems/Problem 6"
(Created page with "==Problem== Many television screens are rectangles that are measured by the length of their diagonals. The ratio of the horizontal length to the height in a standard television ...") |
|||
Line 7: | Line 7: | ||
==Solution== | ==Solution== | ||
− | + | If you divide the television screen into two right triangles, the legs are in the ratio of <math>4 : 3</math>, and we can let one leg be <math>4x</math> and the other be <math>3x</math>. Then we can use the Pythagorean Theorem. | |
− | + | <cmath>\begin{align*}(4x)^2+(3x)^2&=27^2\\ | |
+ | 16x^2+9x^2&=729\\ | ||
+ | 25x^2&=729\\ | ||
+ | x^2&=\frac{729}{25}\\ | ||
+ | x&=\frac{27}{5}\\ | ||
+ | x&=5.4\end{align*}</cmath> | ||
− | + | The horizontal length is <math>5.4\times4=21.6</math>, which is closest to <math>\boxed{\mathrm{(D) \ } 21.5}</math>. | |
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | |||
− | The horizontal length is <math>5.4\ | ||
==See Also== | ==See Also== | ||
{{AMC10 box|year=2003|ab=B|num-b=5|num-a=7}} | {{AMC10 box|year=2003|ab=B|num-b=5|num-a=7}} |
Revision as of 02:15, 10 June 2011
Problem
Many television screens are rectangles that are measured by the length of their diagonals. The ratio of the horizontal length to the height in a standard television screen is . The horizontal length of a "-inch" television screen is closest, in inches, to which of the following?
Solution
If you divide the television screen into two right triangles, the legs are in the ratio of , and we can let one leg be and the other be . Then we can use the Pythagorean Theorem.
The horizontal length is , which is closest to .
See Also
2003 AMC 10B (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 |