a diagonal brace is to be placed in the wall of room, the height (y) of the wall is 8 ft and the wall is 16 ft long (x). What is the exact length of the brace?
Use the Pythagorean Theorem.
x^2 + y^2 = b^2
8^2 + 16^2 = b^2
64 + 256 = b^2
320 = b^2
17.888543 = b
Well, brace yourself for this answer. To find the length of the diagonal brace, we can use the Pythagorean theorem! It states that the square of the hypotenuse (the diagonal brace) is equal to the sum of the squares of the two other sides (the height and the length of the wall). In this case, we have a lovely little right triangle.
So, let's plug in the numbers! The height (y) of the wall is 8 ft and the length (x) is 16 ft. Using the Pythagorean theorem, we can calculate the length of the diagonal brace (let's call it z):
z^2 = x^2 + y^2
z^2 = 16^2 + 8^2
z^2 = 256 + 64
z^2 = 320
Now comes the tricky part - finding the exact length of the brace. Since 320 is not a perfect square, we can't take the square root to find z directly. The exact length of the diagonal brace, therefore, is the square root of 320. It turns out to be a number with lots of decimal places (approx. 17.8885 ft), so we'll leave it as the square root of 320 for now.
And there you have it! The exact length of the brace in your room is the square root of 320. Time to measure it out and get that wall braced up!
To find the exact length of the diagonal brace, we can use the Pythagorean theorem, which relates the lengths of the sides of a right-angled triangle. In this case, the wall forms one side of the triangle, the height of the wall forms the other side, and the diagonal brace forms the hypotenuse.
Using the Pythagorean theorem, we have:
c^2 = a^2 + b^2
where c is the length of the diagonal brace, and a and b are the lengths of the other two sides of the triangle.
In this case, a represents the height of the wall (y) and b represents the length of the wall (x), so we have:
c^2 = y^2 + x^2
Plugging in the values we know, with y = 8 ft and x = 16 ft, we get:
c^2 = 8^2 + 16^2
c^2 = 64 + 256
c^2 = 320
To find the exact length of the brace (c), we need to take the square root of both sides of the equation:
c = sqrt(320)
c ≈ 17.89 ft
Therefore, the exact length of the diagonal brace is approximately 17.89 feet.
To find the exact length of the brace, we can use the Pythagorean theorem, which states that for a right-angled triangle, the square of the length of the hypotenuse (the diagonal brace) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the wall acts as one side of the triangle and the height of the wall acts as the other side. The diagonal brace would be the hypotenuse.
Using the Pythagorean theorem, we can express it as:
diagonal brace^2 = x^2 + y^2
where x is the length of the wall (16 ft) and y is the height of the wall (8 ft).
Plugging in the values, we have:
diagonal brace^2 = (16 ft)^2 + (8 ft)^2
diagonal brace^2 = 256 ft^2 + 64 ft^2
diagonal brace^2 = 320 ft^2
To find the exact length of the brace, we take the square root of both sides:
diagonal brace = √(320 ft^2)
Using a calculator, we can find the square root of 320:
diagonal brace ≈ 17.89 ft
Therefore, the exact length of the diagonal brace is approximately 17.89 feet.