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.
Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The width of the door is 6.26 ft or √(196/5)ft.
The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The size of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides, according to this rule.
Given the length of the rectangular door is two times its width, therefore, the length and width of the rectangular door are,
Width = x
Length = 2x
Since the measure of the diagonal of the rectangular door is 14 feet, therefore, using the Pythagorus theorem we can write,
x² + (2x)² = 14²
x² + 4x² = 196
5x² = 196
x² = 196/5
x = 6.26099 ≈ 6.26ft
Hence, the width of the door is 6.26 ft or √(196/5)ft.
Learn more about Pythagoras' Theorem:
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