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A farmer wishes to put a fence diagonally across a rectangular field. He does not have time to measure the diagonal but already knows the sides of the existing field are 500 m by 1200 m. How much fencing will he need to buy?

Question

A farmer wishes to put a fence diagonally across a rectangular field. He does not have time to measure the diagonal but already knows the sides of the existing field are 500 m by 1200 m. How much fencing will he need to buy?

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Solution

To find the length of the diagonal (which is the amount of fencing the farmer will need), we can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Here are the steps:

  1. Square the length of the first side: 500^2 = 250,000
  2. Square the length of the second side: 1200^2 = 1,440,000
  3. Add these two results together: 250,000 + 1,440,000 = 1,690,000
  4. Take the square root of this sum to find the length of the diagonal: √1,690,000 = 1300 meters

So, the farmer will need to buy 1300 meters of fencing.

This problem has been solved

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