Question

hidden pythagorean theorem p2

1. tom & jerry are at the park when they see a hot dog vendor. tom doesnt want to ruin her shoes on the wet grass, so she walks 50 meters along the short side of the park, and then 100 meters along the long side to reach the vendor. jerry is starving, so he runs straight to the vendor across the grass. who has to go the farthest, and by how much?

Explanation:

Step1: Calculate Tom's distance

Tom walks \(50 + 100=150\) meters.

Step2: Calculate Jerry's distance

Using the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = 50\) and \(b = 100\).
So \(c=\sqrt{50^{2}+100^{2}}=\sqrt{2500 + 10000}=\sqrt{12500}=50\sqrt{5}\approx50\times2.24 = 112\) meters.

Step3: Find the difference

The difference is \(150-112 = 38\) meters.

Answer:

Tom has to go the farthest, by 38 meters.