Leah's rectangular driveway is 48 feet long and 14 feet wide. With sidewalk chalk, Leah drew a straight diagonal line on her driveway from one corner to the opposite corner.

How long is the diagonal line Leah drew?
25 feet
46 feet
50 feet
62 feet

1 answer

To find the length of the diagonal line Leah drew, we can use the Pythagorean theorem. The formula is:

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

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

In Leah's case:

  • \( a = 48 \) feet (length of the driveway)
  • \( b = 14 \) feet (width of the driveway)

Now we can calculate \( c \):

\[ c = \sqrt{48^2 + 14^2} \] \[ c = \sqrt{2304 + 196} \] \[ c = \sqrt{2500} \] \[ c = 50 \text{ feet} \]

So, the length of the diagonal line Leah drew is 50 feet.