A wall is supported by a brace 10 feet long. If one end of the brace is placed 6 feet from the base of the wall, how many feet up the wall does the brace reach?

Think of the right triangle frmed by the wall, the floor and the brace, and use the Pythagorean theorem. The brace is the hypotenuse

To find out how many feet up the wall the brace reaches, we can use the Pythagorean theorem. The theorem 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 brace is the hypotenuse, and we know the lengths of the other two sides. The length of one side is 10 feet (the length of the brace), and the distance from the base of the wall to one end of the brace is 6 feet.

Let's label the length up the wall that the brace reaches as x. We can set up the equation as follows:

x^2 + 6^2 = 10^2

Simplifying the equation:

x^2 + 36 = 100

Subtracting 36 from both sides:

x^2 = 100 - 36

x^2 = 64

Taking the square root of both sides:

x = √64

Since 8 * 8 = 64, the square root of 64 is 8.

Therefore, the brace reaches 8 feet up the wall.

To find out how many feet up the wall the brace reaches, 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 brace acts as the hypotenuse, with one end placed 6 feet from the base of the wall. We can consider this end as one of the legs of the right triangle.

Let's label the length up the wall that the brace reaches as "x". Therefore, the other leg of the right triangle would be "x" as well.

According to the Pythagorean theorem, we have the equation:

(Length of the hypotenuse)^2 = (Length of one leg)^2 + (Length of the other leg)^2

Substituting the given values, we have:

10^2 = 6^2 + x^2

Simplifying the equation:

100 = 36 + x^2

Rearranging the equation:

x^2 = 100 - 36

x^2 = 64

Taking the square root of both sides, we have:

x = 8

Therefore, the brace reaches 8 feet up the wall.

this is a Pythagorean triple

... in this case a 3-4-5 , multiplied by 2 ... 6-8-10