Difference between revisions of "2009 UNCO Math Contest II Problems/Problem 5"
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== Solution == | == Solution == | ||
− | + | We see that the area of triangle A and B is 450 from the area of square A doubled. Noticing that all triangles made are 45-45-90,we write the area of the figure in terms of s, a side of square b. Writing this as (s^2)/4 + 2s^2 = 450, solving by algebra is trivial and we see s is <math>\sqrt{200}</math>, and the area of square b is therefore <math>\boxed{200}</math>. | |
== See also == | == See also == |
Latest revision as of 02:35, 29 January 2019
Problem
The two large isosceles right triangles are congruent. If the area of the inscribed square is square units, what is the area of the inscribed square ?
Solution
We see that the area of triangle A and B is 450 from the area of square A doubled. Noticing that all triangles made are 45-45-90,we write the area of the figure in terms of s, a side of square b. Writing this as (s^2)/4 + 2s^2 = 450, solving by algebra is trivial and we see s is , and the area of square b is therefore .
See also
2009 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
All UNCO Math Contest Problems and Solutions |