Mary wants to cut across a rectangular lot rather than walk around it. The lot is 120 feet long and 50 feet wide. Mary walks diagonally across the lot, how many feet is the short cut?

Answer 1

To find the distance Mary will walk diagonally across the rectangular lot, we can use the Pythagorean theorem. The formula is:

\[ c = \sqrt{a^2 + b^2} \]

where \(c\) is the length of the diagonal, \(a\) is the length of the rectangle, and \(b\) is the width of the rectangle.

In this case, the lot is 120 feet long and 50 feet wide. So, we can substitute \(a = 120\) feet and \(b = 50\) feet into the formula:

\[ c = \sqrt{120^2 + 50^2} \]

Calculating \(120^2\) and \(50^2\):

\[ 120^2 = 14400 \] \[ 50^2 = 2500 \]

Now add these two results together:

\[ 14400 + 2500 = 16900 \]

Now take the square root of \(16900\):

\[ c = \sqrt{16900} = 130 \]

Therefore, the distance Mary will walk diagonally across the lot is 130 feet.

Answer 2

did you use the Pythagoreaon theorem portfolio

Answer 3

Yes, I used the Pythagorean theorem to calculate the diagonal distance across the rectangular lot. The theorem 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 the context of the rectangular lot, the length (120 feet) and width (50 feet) of the lot represent the two legs of the right triangle, and the diagonal represents the hypotenuse.

Here's a quick recap of the steps I took using the Pythagorean theorem:

1. Identify the two legs of the triangle:

   • Length \(a = 120\) feet
   • Width \(b = 50\) feet

2. Use the Pythagorean theorem: \[ c = \sqrt{a^2 + b^2} \]

3. Substitute the values and calculate: \[ c = \sqrt{120^2 + 50^2} \]

4. Calculate \(120^2\) and \(50^2\):

   • \(120^2 = 14400\)
   • \(50^2 = 2500\)

5. Add these values: \[ 14400 + 2500 = 16900 \]

6. Find the square root to get the diagonal: \[ c = \sqrt{16900} = 130 \]

So, the diagonal distance (the shortcut) is 130 feet. If you have a specific aspect of the Pythagorean theorem or any further questions about how it applies here, feel free to ask!