The rectangular section of fencing below is reinforced with wood nailed across the diagonal of the rectangle. What is the length of the diagonal?
A rectangular fence has a diagonal board dividing it into 2 right triangles. The triangle has a leg measuring 6 feet and, a leg measuring 8 feet.
The diagonal of the rectangle is the hypotenuse of the right triangle. The hypotenuse can be calculated using the Pythagorean theorem: c^2 = a^2 + b^2, where c is the hypotenuse, a is the first leg, and b is the second leg. In this case, c^2 = 6^2 + 8^2 = 36 + 64 = 100. The diagonal of the rectangle is the square root of 100, which is 10 feet.
To find the length of the diagonal of the rectangular section of fencing, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides.
In this case, one leg of the right triangle measures 6 feet and the other leg measures 8 feet. Let's denote the length of the diagonal as "d".
According to the Pythagorean theorem, we have the equation:
d^2 = 6^2 + 8^2
Simplifying the equation:
d^2 = 36 + 64
d^2 = 100
To find the value of "d", we can take the square root of both sides of the equation:
d = √100
d = 10 feet
Therefore, the length of the diagonal of the rectangular section of fencing is 10 feet.
To find the length of the diagonal, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the two legs of the right triangle are given as 6 feet and 8 feet. Let's call the length of the diagonal "d".
According to the Pythagorean theorem, we have:
d^2 = 6^2 + 8^2
Simplifying the equation:
d^2 = 36 + 64
d^2 = 100
Taking the square root of both sides:
d = √100
d = 10
Therefore, the length of the diagonal is 10 feet.