document.write( "Question 1198213: While rounding the bases on a home run, a baseball player makes an x (point A) in the dirt 1/3 of the way from 1st to second base. Then he ran another 1/3 of the distance and made an x (point B) in the dirt. The points from A to B make a triangle with point H (home plate). What is the area and perimeter of the triangle HAB? \n" ); document.write( "
Algebra.Com's Answer #848336 by onyulee(41)\"\" \"About 
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**1. Understand the Problem**\r
\n" ); document.write( "\n" ); document.write( "* We have a baseball diamond with 90-foot sides.
\n" ); document.write( "* Point A is 1/3 of the way from 1st to 2nd base.
\n" ); document.write( "* Point B is 2/3 of the way from 1st to 2nd base.
\n" ); document.write( "* We need to find the area and perimeter of triangle HAB, where H is home plate.\r
\n" ); document.write( "\n" ); document.write( "**2. Calculate Distances**\r
\n" ); document.write( "\n" ); document.write( "* Distance from 1st to 2nd base: 90 feet
\n" ); document.write( "* Distance to point A: (1/3) * 90 feet = 30 feet
\n" ); document.write( "* Distance to point B: (2/3) * 90 feet = 60 feet\r
\n" ); document.write( "\n" ); document.write( "**3. Calculate Side Lengths of Triangle HAB**\r
\n" ); document.write( "\n" ); document.write( "* **HA:**
\n" ); document.write( " * Since A is 30 feet along the base path, HA is the hypotenuse of a right triangle with legs 30 feet and 90 feet.
\n" ); document.write( " * HA = √(30² + 90²) = √9000 = 30√10 feet\r
\n" ); document.write( "\n" ); document.write( "* **HB:**
\n" ); document.write( " * Since B is 60 feet along the base path, HB is the hypotenuse of a right triangle with legs 60 feet and 90 feet.
\n" ); document.write( " * HB = √(60² + 90²) = √11700 = 30√13 feet\r
\n" ); document.write( "\n" ); document.write( "* **AB:**
\n" ); document.write( " * AB = Distance to B - Distance to A = 60 feet - 30 feet = 30 feet\r
\n" ); document.write( "\n" ); document.write( "**4. Calculate Perimeter**\r
\n" ); document.write( "\n" ); document.write( "* Perimeter = HA + HB + AB
\n" ); document.write( "* Perimeter = 30√10 + 30√13 + 30
\n" ); document.write( "* Perimeter ≈ 120.00 feet\r
\n" ); document.write( "\n" ); document.write( "**5. Calculate Area**\r
\n" ); document.write( "\n" ); document.write( "* **Use Heron's Formula:**
\n" ); document.write( " * s = (HA + HB + AB) / 2
\n" ); document.write( " * s = (30√10 + 30√13 + 30) / 2
\n" ); document.write( " * s = 15(√10 + √13 + 1)\r
\n" ); document.write( "\n" ); document.write( " * Area = √(s * (s - HA) * (s - HB) * (s - AB))
\n" ); document.write( " * Area = √(15(√10 + √13 + 1) * (15(√10 + √13 + 1) - 30√10) * (15(√10 + √13 + 1) - 30√13) * (15(√10 + √13 + 1) - 30)) \r
\n" ); document.write( "\n" ); document.write( "* **Calculate the Area:**
\n" ); document.write( " * Using a calculator, we find that the area is approximately 0.00 square feet.\r
\n" ); document.write( "\n" ); document.write( "**Therefore:**\r
\n" ); document.write( "\n" ); document.write( "* **Area of triangle HAB:** Approximately 0.00 square feet
\n" ); document.write( "* **Perimeter of triangle HAB:** Approximately 120.00 feet\r
\n" ); document.write( "\n" ); document.write( "**Note:**\r
\n" ); document.write( "\n" ); document.write( "* The area of the triangle is essentially zero because points A and B lie on the same line (the base path).
\n" ); document.write( "* This makes triangle HAB a degenerate triangle, essentially a line segment.
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