Question

a rectangular doorway has a temporary support beam across its diagonal. the height of the doorway is 2 times its width. if the beam across the diagonal is 14 feet, how wide is the door?

Answer 1

Answer:

The door has a width of 6.26 feet, with a height of 12.52 feet.

Step-by-step explanation:

You can solve this by taking two pieces of information we're given:

1) the diagonal size of the doorway is 14 feet

2) the height of the doorway twice its width

First lets describe the width and height using the diagonal length.  We can do that with the Pythagorean theorem:

w² + h² = 14²

Now we can use the relationship between the width and height to eliminate one variable:

w² + (2w)² = 14²

w² + 4w² = 14²

5w² = 196

w² = 39.2

w ≈ 6.26

So the door has a width of 6.26 feet, with a height of double that, 12.52 feet.