Question

8 In ancient Egypt, when the Nile flooded, it often erased the boundaries between landowners. An accurate surveying process was necessary in order to re-establish property lines. Land surveyors used Pythagoras' theorem to verify that property lines were correctly drawn by calculating how long they should be. Two farmers occupy a property that is in the shape of a rectangle. Their property line is the diagonal of the rectangle. Find the length of the property line if the sides of the property measure 48 m and 55 m.​

Answer 1

The length of the property line (diagonal) of the rectangle can be found using the Pythagorean theorem. By substituting the given values into the theorem formula and solving for 'c', we find that the length of the property line is approximately 73 meters.

Step-by-step explanation:

The length of the property line, which is the diagonal of a rectangle, can be found using the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the two sides of the rectangle are 48 m and 55 m. Let's label them as 'a' and 'b'.

Using the Pythagorean theorem, we have:

c² = a² + b²

where 'c' is the length of the property line (diagonal).

Substituting the given values:

c² = 48² + 55²

c² = 2304 + 3025

c² = 5329

Solving for 'c' by taking the square root of both sides:

c ≈ √5329

c ≈ 73 m

Therefore, the length of the property line is approximately 73 meters.