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Calculate the direct distance from home to school using the Pythagorean theorem, given a 3 km west and 4 km south displacement.

Mathematics

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Answer

5 km5 \text{ km}

Step-by-step solution

2 steps

a) What is the distance from your home to school using the direct path?

  1. Recall the distances from the previous problem.

    The boda-boda traveled 3 km west and 4 km south. The "direct path" refers to the straight-line distance, which is the hypotenuse of the right-angled triangle formed by these two segments. This is the same as the "shortcut path" calculated previously.

  2. Use the Pythagorean theorem.

    Direct path=(3 km)2+(4 km)2\text{Direct path} = \sqrt{(3 \text{ km})^2 + (4 \text{ km})^2} Direct path=9 km2+16 km2\text{Direct path} = \sqrt{9 \text{ km}^2 + 16 \text{ km}^2} Direct path=25 km2\text{Direct path} = \sqrt{25 \text{ km}^2} Direct path=5 km\text{Direct path} = \boxed{5 \text{ km}}

    For parts b) and c), I need more information. Please send the details about the school expenses, scholarship amount, your aunt's budget, and the different payment options.

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