Math  /  Geometry

Question(2) A rectangular garden is 25 bug 35 meters wide. What is the distance a farmer will travel if he walks from one correr to the opposite?
Answer: \qquad meters

Studdy Solution

STEP 1

1. The garden is a rectangle with dimensions 25 meters by 35 meters.
2. The farmer walks diagonally from one corner of the rectangle to the opposite corner.
3. We need to calculate the length of the diagonal.

STEP 2

1. Identify the dimensions of the rectangle.
2. Use the Pythagorean Theorem to calculate the diagonal distance.

STEP 3

Identify the dimensions of the rectangle. The rectangle is 25 meters wide and 35 meters long.

STEP 4

Apply the Pythagorean Theorem to find the diagonal distance. The diagonal forms the hypotenuse of a right triangle with the sides of the rectangle as the other two sides.
The Pythagorean Theorem is given by:
c=a2+b2 c = \sqrt{a^2 + b^2}
where a a and b b are the lengths of the rectangle's sides, and c c is the diagonal.

STEP 5

Substitute the known values into the Pythagorean Theorem:
c=(25)2+(35)2 c = \sqrt{(25)^2 + (35)^2}

STEP 6

Calculate the squares of the side lengths:
c=625+1225 c = \sqrt{625 + 1225}

STEP 7

Add the results of the squares:
c=1850 c = \sqrt{1850}

STEP 8

Simplify the square root if possible. In this case, we can leave it as is or approximate it:
c185043.01 c \approx \sqrt{1850} \approx 43.01
The distance the farmer will travel diagonally across the garden is approximately:
43.01 \boxed{43.01} meters

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