Altitude on Hypotenuse

Front

What is the altitude on the hypotenuse in a right triangle?

Back

The altitude on the hypotenuse is a line segment drawn from the right angle to the hypotenuse, forming two smaller right triangles that are similar to the original triangle.

Front

How do you calculate the area of a triangle using the altitude?

Back

Area = 1/2 * base * height, where the base is the length of the hypotenuse and the height is the length of the altitude.

Front

What is the relationship between the altitude and the segments it creates on the hypotenuse?

Back

The altitude divides the hypotenuse into two segments, and the product of the lengths of these segments is equal to the square of the length of the altitude.

Front

If the hypotenuse is 10 units and the altitude is 6 units, what are the lengths of the segments on the hypotenuse?

Back

Let the segments be x and y. Then, x * y = 6^2 = 36. The sum of x and y must equal 10. Solve the equations to find x and y.

Front

What is the geometric mean in relation to the altitude on the hypotenuse?

Back

The length of the altitude is the geometric mean of the lengths of the two segments it creates on the hypotenuse.

Front

If the segments on the hypotenuse are 4 units and 6 units, what is the length of the altitude?

Back

The altitude can be found using the formula: altitude = √(4 * 6) = √24 = 2√6.

Front

What is the Pythagorean theorem?

Back

In a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): c² = a² + b².

Front

How can you use the Pythagorean theorem to find the altitude on the hypotenuse?

Back

You can use the Pythagorean theorem to find the lengths of the sides of the smaller triangles formed by the altitude and then apply the area formula.

Front

What is the formula for the area of a triangle using the hypotenuse and altitude?

Back

Area = 1/2 * hypotenuse * altitude.

Front

If the area of a triangle is 30 square units and the hypotenuse is 10 units, what is the altitude?

Back

Using the area formula: 30 = 1/2 * 10 * altitude, solve for altitude: altitude = 6 units.