Question

Terry needs to carry a pole that

is 10 feet tall through a
rectangular doorway that
measures 6 feet by q feet. Will
the pole fit diagonally through the

doorway? Explain.
6 ft
9 ft

Answer 1

Yes, The pole will fit through the door because the diagonal width of the door is 10.8 feet, which is longer than the length of the pole.

Explanation:

Using the Pythagorean Theorem, (
`a^2+b^2=c^2` ) we can measure the hypotenuse of a right triangle. Since the doorway is a rectangle, and a rectangle cut diagonally is a right triangle, we can use Pythagorean Theorem to measure the diagonal width of the doorway.

Plug in the values of the length and width of the door for a and b. The c value will represent the diagonal width of the doorway:

`6^2+9^2=c^2`

`36+81=c^2`

`117=c^2`

Since 117 is equal to the value of c multiplied by c, we must find the square root of 117 to find the value of c.

`√(117) =10.8`

`10.8=c`

Yes, The pole will fit through the door because the diagonal width of the door is 10.8 feet, which is longer than the length of the pole, measuring 10 feet.