A doorway is 8 feet high and 4 feet wide. A square piece of plywood needs to be moved through the doorway. The plywood is 10 feet long and 10 feet wide. The door is a rectangle with a height of 8 feet, and a width of 4 feet. A dotted line shows the diagonal.

Will the piece of plywood fit through the door if it is tilted diagonally?

A. No, because the length of the diagonal is close to 9 feet.

B. No, because the height of the door is less than 10 feet.

C. Yes, because the length of the diagonal is close to 11 feet.

D. Yes, because the sum of the height and width of the door is greater than 10 feet.

Question

Mathematics

Dean Short

24 January, 14:05

A doorway is 8 feet high and 4 feet wide. A square piece of plywood needs to be moved through the doorway. The plywood is 10 feet long and 10 feet wide. The door is a rectangle with a height of 8 feet, and a width of 4 feet. A dotted line shows the diagonal.

Will the piece of plywood fit through the door if it is tilted diagonally?

A. No, because the length of the diagonal is close to 9 feet.

B. No, because the height of the door is less than 10 feet.

C. Yes, because the length of the diagonal is close to 11 feet.

D. Yes, because the sum of the height and width of the door is greater than 10 feet.

+1

Answers (1)

Know the Answer?

Meghan Terry · Answer 1

By the Pythagorean Theorem:

d^2=x^2+y^2

d^2=8^2+4^2

d^2=64+16

d^2=80

d=√80

d=4√5 ft

d≈8.944

So

A. No because the diagonal is close to 9 feet.