A walkman path is shaped like a rectangle with a width 7 times its length l. What is a simplified expression for the distance between opposite corners of the walking path
you are just finding the hypotenuse of a right-angled triangle with sides l and 7l
Hyp^2 = l^2 + (7l)^2 = 50l^2
hyp = √(50l^2)
= 5√2 l
To find the distance between opposite corners of the walkman path, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, since the walkman path is shaped like a rectangle, we have a right triangle formed by its length (l), width (7l), and the diagonal (distance between opposite corners).
Using the Pythagorean theorem, we have:
(diagonal)^2 = (length)^2 + (width)^2
Let's substitute the values we have:
(diagonal)^2 = l^2 + (7l)^2
Simplifying:
(diagonal)^2 = l^2 + 49l^2
(diagonal)^2 = 50l^2
Taking the square root of both sides to find the diagonal:
diagonal = sqrt(50l^2)
Further simplifying:
diagonal = sqrt(50) * sqrt(l^2)
Since sqrt(50) = sqrt(25) * sqrt(2) = 5 * sqrt(2), we have:
diagonal = 5 * sqrt(2) * l
So, a simplified expression for the distance between opposite corners of the walkman path is 5 * sqrt(2) * l.