A rectangular hall is 55 feet long and 48 feet wide. How long is a walkway along the diagonal?
60 feet
65 feet
73 feet
70 feet
To find the length of the walkway along the diagonal, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the length of the hall (a) is the width of the triangle, the width of the hall (b) is the height of the triangle, and the length of the walkway (c) is the hypotenuse.
Using the Pythagorean theorem:
c^2 = a^2 + b^2
Substituting in the values:
c^2 = 55^2 + 48^2
c^2 = 3025 + 2304
c^2 = 5329
Taking the square root of both sides to find c:
c = sqrt(5329)
c ≈ 73
Therefore, the length of the walkway along the diagonal is approximately 73 feet.
So the answer is 73 feet.
A rectangular garden measures 24 ft by 7 ft. A sidewalk runs diagonally from one corner to the opposite corner. Find the length of the sidewalk.
17 ft
27 ft
25 ft
35 ft
To find the length of the sidewalk, we again can use the Pythagorean theorem.
In this case, the length of the garden (a) is the width of the triangle, the width of the garden (b) is the height of the triangle, and the length of the sidewalk (c) is the hypotenuse.
Using the Pythagorean theorem:
c^2 = a^2 + b^2
Substituting in the values:
c^2 = 24^2 + 7^2
c^2 = 576 + 49
c^2 = 625
Taking the square root of both sides to find c:
c = sqrt(625)
c = 25
Therefore, the length of the sidewalk is 25 feet.
So the answer is 25 ft.
Mark made a sandwich that was 5 inches long and 7 inches high. If he cuts the sandwich in half, what would be the diagonal length of the sandwich?
25 inches
8.6 inches
49 inches
74 inches
To find the diagonal length of the sandwich after it is cut in half, we can again use the Pythagorean theorem.
In this case, the length of the sandwich (a) is the width of the triangle, the height of the sandwich (b) is the height of the triangle, and the diagonal length of the sandwich (c) is the hypotenuse.
Using the Pythagorean theorem:
c^2 = a^2 + b^2
Substituting in the values:
c^2 = (5/2)^2 + 7^2
c^2 = (25/4) + 49
c^2 = 6.25 + 49
c^2 = 55.25
Taking the square root of both sides to find c:
c = sqrt(55.25)
c ≈ 7.43
Therefore, the diagonal length of the sandwich after it is cut in half is approximately 7.43 inches.
So the answer is 7.43 inches.
To find the length of the walkway along the diagonal, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right 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 hall form the legs of a right triangle, and the length of the walkway is the hypotenuse. So, we can use the Pythagorean theorem to find the length of the walkway.
Let's call the length of the walkway "d" (in feet).
According to the Pythagorean theorem, we have:
d^2 = (length)^2 + (width)^2
Substituting the given values, we get:
d^2 = 55^2 + 48^2
Calculating the right side of the equation:
d^2 = 3025 + 2304
d^2 = 5329
Taking the square root of both sides to solve for "d":
d = √5329
The square root of 5329 is approximately 72.99.
Therefore, the approximate length of the walkway along the diagonal is 73 feet.
So, the answer is 73 feet.
To find the length of the walkway along the diagonal of a rectangular hall, 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 the width of the hall form the two sides of a right-angled triangle, and the walkway is the hypotenuse. Let's label the length of the walkway as "d".
Using the Pythagorean theorem, the equation will be:
Length^2 + Width^2 = Diagonal^2
Plugging in the values, we have:
55^2 + 48^2 = d^2
Simplifying:
3025 + 2304 = d^2
5329 = d^2
Taking the square root of both sides:
d = √5329
Calculating the square root, the diagonal length can be determined:
d ≈ 73 feet
Therefore, the correct answer is 73 feet.