Two boys are running track. They decide to start in the northwest corner and go opposite directions around the rectangular track. If the width of the track is 150 yards and the diagonal is 240 yards, what is the length of the track?
283.01 yards
210 yards
155 yards
125 yards
Let's call the length of the track $x$. Since the diagonal of the rectangular track is 240 yards, we can use the Pythagorean Theorem to find the length of the track.
The Pythagorean Theorem states that for any right triangle with legs of length $a$ and $b$ and hypotenuse of length $c$, the relationship $a^2 + b^2 = c^2$ holds.
In this case, the legs of the right triangle are the width of the track and the length of the track, which are 150 yards and $x$ yards, respectively. The hypotenuse is the diagonal of the track, which is 240 yards.
Using the Pythagorean Theorem, we have:
$150^2 + x^2 = 240^2$
Simplifying, we get:
$22500 + x^2 = 57600$
Subtracting 22500 from both sides, we get:
$x^2 = 57600 - 22500$
$x^2 = 35100$
Taking the square root of both sides, we get:
$x = \sqrt{35100}$
$x \approx 187.36$
Therefore, the length of the track is approximately 187.36 yards. None of the given answer choices match this result, so it seems there may be an error in the problem statement.
To find the length of the track, we can use the Pythagorean theorem since we have the width and the diagonal. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides (width and length).
Let's denote the length of the track as "l". According to the given information, the width is 150 yards and the diagonal is 240 yards.
Using the Pythagorean theorem:
l² = 240² - 150²
l² = 57600 - 22500
l² = 35100
Taking the square root of both sides to find "l":
l = √35100
l ≈ 187.16 yards (rounded to two decimal places)
Therefore, the length of the track is approximately 187.16 yards. None of the answer choices provided exactly matches this length, so it seems there is an error in the answer choices.