# The right triangle altitude theorem + real numbers - math problems

The altitude to the hypotenuse is the geometric mean of the two segments of the hypotenuse. Each leg of the right triangle is the mean proportional of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg.

$h = \sqrt{c_1 c_2}$

Also known as a geometric mean theorem. Geometric mean theorem is a special case of the chord theorem.

#### Number of problems found: 6

• Rectangle
In rectangle ABCD with sides |AB|=19, |AD|=16 is from point A guided perpendicular to the diagonal BD, which intersects at point P. Determine the ratio ?.
• Right Δ
A right triangle has the length of one leg 11 cm and length of the hypotenuse 61 cm. Calculate the height of the triangle.
• Area of RT
Calculate the area of a right triangle that hypotenuse has length 14, and one hypotenuse segment has length 5.
• Hypotenuse and height
In a right triangle is length of the hypotenuse c = 56 cm and height hc = 4 cm. Determine the length of both trangle legs.
• Area of RT
In the right triangle has orthogonal projections of legs to the hypotenuse lengths 7 cm and 12 cm. Determine the area of ​​this triangle.
• Euclid1
Right triangle has hypotenuse c = 27 cm. How large sections cuts height hc=3 cm on the hypotenuse c?

We apologize, but in this category are not a lot of examples.
Do you have an interesting mathematical word problem that you can't solve it? Submit a math problem, and we can try to solve it.

We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...