Difference between revisions of "User:Jeff10"
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I have constructed a rectangular figure. After drawing both diagonal, I will have constructed four congruent triangles. The length of the hypotenuses are both 17 units. Given that the length and width of this rectangle are both integer lengths, what is the area of one of the four triangles created? After you have found that, find the lengths and angles of the triangle. You may use a calculator if necessary. | I have constructed a rectangular figure. After drawing both diagonal, I will have constructed four congruent triangles. The length of the hypotenuses are both 17 units. Given that the length and width of this rectangle are both integer lengths, what is the area of one of the four triangles created? After you have found that, find the lengths and angles of the triangle. You may use a calculator if necessary. | ||
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SOLUTION | SOLUTION | ||
Given the hypotenuse is 17 units, you may want to list all of the possibilities such that a square and a number added together is 289. A better way is to use the difference of squares and actually hunt for the values, which are length of 15 and width of 8. When you multiply them together, you will get the area of the rectangle, which is 120, but you want the area of one of the four congruent triangles, which is 30. With the knowledge of trigonmetry, you can use sine or cosine to find the angles. | Given the hypotenuse is 17 units, you may want to list all of the possibilities such that a square and a number added together is 289. A better way is to use the difference of squares and actually hunt for the values, which are length of 15 and width of 8. When you multiply them together, you will get the area of the rectangle, which is 120, but you want the area of one of the four congruent triangles, which is 30. With the knowledge of trigonmetry, you can use sine or cosine to find the angles. | ||
Revision as of 14:04, 2 November 2011
Please do not edit this page without permission.
PROBLEM I have constructed a rectangular figure. After drawing both diagonal, I will have constructed four congruent triangles. The length of the hypotenuses are both 17 units. Given that the length and width of this rectangle are both integer lengths, what is the area of one of the four triangles created? After you have found that, find the lengths and angles of the triangle. You may use a calculator if necessary.
SOLUTION
Given the hypotenuse is 17 units, you may want to list all of the possibilities such that a square and a number added together is 289. A better way is to use the difference of squares and actually hunt for the values, which are length of 15 and width of 8. When you multiply them together, you will get the area of the rectangle, which is 120, but you want the area of one of the four congruent triangles, which is 30. With the knowledge of trigonmetry, you can use sine or cosine to find the angles.
