Question

Bethany and Andreas live two blocks apart, and an empty lot lies south of each of their blocks. They both walk diagonally through the empty lots to get to their school, which is about halfway between and 1 block south of their homes. The empty lot that Bethany walks through is 500 feet by 1,200 feet. The empty lot that Andreas walks through is 800 feet by 1,500 feet. How much farther is Andreas' diagonal path than Behany's? *

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Answer 1

Find the hypotenuse of both the lots:

• Bethany's lot:

1. 500² + b² = 1200² (Simplify)
2. 250000 + b² = 1440000 (Isolate b² by subtracting)
3. b² = 1190000 (Take the square root)
4. b = 1090.87

• Andrea's lot:

1. 800² + b² = 1500² (Simplify)
2. 640000 + b² = 2250000 (Isolate b² by subtracting)
3. b² = 1610000 (Take the square root)
4. b = 1268.86

Subtract: 1268.86 - 1090.87 = 177.99 ft.

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