Final answer:
The diagonal length of a TV that is 20 inches wide and 15 inches high is 25 inches, as calculated using the Pythagorean theorem. When crossing a lawn 24 meters long and 10 meters wide diagonally, the walk is 8 meters shorter than walking along the two adjacent sides.
Step-by-step explanation:
Television Screen Diagonal
To find the length of the diagonal of a television screen that is 20 inches wide and 15 inches high, we can use the Pythagorean theorem, which states that in a right-angled 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 (the two legs). In this case, the width and height of the TV screen are the legs, and the diagonal is the hypotenuse.
The formula is: c^2 = a^2 + b^2, where 'c' is the diagonal, and 'a' and 'b' are the width and height, respectively.
Using the provided measurements,
c^2 = 20^2 + 15^2
c^2 = 400 + 225
c^2 = 625
c = √625
c = 25 inches
Therefore, the diagonal of the TV is 25 inches.
Walk Across the Lawn
To find out how much shorter the walk is if one walks diagonally across the lawn, rather than along two adjacent sides, we use the same Pythagorean theorem:
c^2 = a^2 + b^2, with 'a' being 24 meters and 'b' being 10 meters.
c^2 = 24^2 + 10^2
c^2 = 576 + 100
c^2 = 676
c = √676
c = 26 meters
The walk along two adjacent sides would be
a + b = 24 + 10 = 34 meters, so the walk is shorter by
34 meters - 26 meters = 8 meters when walking diagonally across the lawn.