Question

A soccer field is 90 meters wide and 120 meters long.The coach asked the players to run from corner to corner diagonally across.What is the diagonal distance?

Answer 1

The length of diagonal is 150 meters

Solution:

Given that soccer field is 90 meters wide and 120 meters long

The coach asked the players to run from corner to corner diagonally across

To find: length of diagonal

The figure is attached below

Let ABCD be a rectangle with BD as diagonal

From given,

length = DC = 120 meters

width = BC = 90 meters

The diagonal and two sides of rectangle forms a right angled triangle with diagonal as hypotenuse

Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.

By above definition, for right angled triangle DCB

$BD^2 = BC^2 + DC^2$

$BD^2 = 90^2 + 120^2\\\\BD^2 = 8100 + 14400\\\\BD^2 = 22500$

Taking square root on both sides,

$BD = \sqrt{22500}\\\\BD = 150$

Thus length of diagonal is 150 meters