A rectangular park is 200 m by 300 m. If Blake runs along the diagonal of the park, how far will he run? Give your answer to the nearest metre.
√(200^2 + 300^2) = 100√(2^2+3^2) = 100√13
Well, if Blake runs along the diagonal of the rectangular park, he better hope there are no squirrels causing any major detours! But let's get to the math part. We can use the Pythagorean theorem here, which tells us that the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the length of one side is 200 m and the other side is 300 m. So, using the theorem, we have:
(200^2) + (300^2) = c^2
Simplifying that gives us:
40,000 + 90,000 = c^2
And after the little addition party:
130,000 = c^2
Taking the square root of both sides, we find that the length of the diagonal, c, is approximately 360.55 m.
So, Blake will run approximately 361 meters if he follows the diagonal path. And let's hope no clowns pop out of the bushes to join him along the way! Ha-ha!
To find the distance Blake will run along the diagonal of the rectangular park, we can use the Pythagorean theorem.
The Pythagorean theorem 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 other two sides.
In this case, the length and width of the park form the two sides of the right-angled triangle, and the diagonal is the hypotenuse.
Let's denote the length of the park as "L" and the width as "W". In this case, L = 300 m and W = 200 m.
Using the Pythagorean theorem, we can calculate the length of the diagonal (D) as follows:
D^2 = L^2 + W^2
D^2 = 300^2 + 200^2
D^2 = 90000 + 40000
D^2 = 130000
Taking the square root of both sides to find D:
D = sqrt(130000)
D ≈ 360.56 m
Therefore, Blake will run approximately 361 meters along the diagonal of the park.
To find the distance Blake will run along the diagonal of the park, we can use the Pythagorean theorem. The Pythagorean theorem 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 other two sides.
In this case, the length and width of the rectangular park form the two sides of a right-angled triangle, and the diagonal is the hypotenuse. Therefore, we can use the Pythagorean theorem to calculate the diagonal.
Let's denote the length of the park as "a" and the width as "b". In this case, a = 200 m and b = 300 m. Using the Pythagorean theorem, we have:
c^2 = a^2 + b^2,
where c is the length of the diagonal (the hypotenuse).
Substituting the given values, we have:
c^2 = 200^2 + 300^2,
c^2 = 40000 + 90000,
c^2 = 130000.
Taking the square root of both sides, we get:
c = square root of 130000.
Calculating the square root of 130000 gives us approximately 360.56.
Therefore, Blake will run approximately 360.56 meters along the diagonal of the park. Rounded to the nearest meter, he will run approximately 361 meters.