Geometry
posted by Camile .
If the length of the altitude of the hypotenuse of a right triangle is 8, and the length of the hypotenuse is 20, what are the lengths of the segments of the hypotenuse? (Let x and 20x be the lengths of the segments of the hypotenuse.)

Geometry 
Reiny
you will have similar triangles, and it can be shown quite easily that
x(20x) = 82
x^2 + 20x  64 = 0
x^2  20x + 64 = 0
(x16)(x4) = 0
x = 16 or x = 4
if one part is 16, the other is 2016 or 4
if one part is 4, the other is 204 = 16
so the two segments are 16 and 4 
Geometry 
tchrwill
The altitude to the hypotenuse of a right triangle is the geometric mean between the segments of the hypotenuse created by the point where the altitude intersects the hypotenuse or h^2 = xy.
x and y are the two segments of the hypotenuse.
Therefore, h^2 = 64 = xy and x + y = 20.
64 = y(20  y) or y^2  20y + 64 = 0.
Then, x = [20+/sqrt(400  256)]/2 or y = 16 making x = 4.
Respond to this Question
Similar Questions

math/geometry
complete the statements: To find the length of the hypotenuse of a 454590 triangle, multiply the length of one of the legs by:? 
Geometry
In right triangle ABC, the median to the hypotenuse has length 15 units and the altitude to the hypotenuse has length 12 units. What is the legth of the shorter leg of triangle ABC? 
geometry
The altitude upon the hypotenuse of a right triangle divides the hypotnuse into segments of 3 and 12. find the length of the altitude 
Geometry
The altitude of the hypotenuse of a right triangle divides the hypotenuse into segments of lengths 14 and 8. What is the length of the altitude? 
math
The legs of a right triangle are 3 and 4 units long. Find the lengths, to the nearest tenth, of the segments into which the bisector of the right angle divides the hypotenuse. (Hint: Draw a picture of the triangle, label one segment … 
Geometry
The altitude to the hypotenuse of a right triangle ABC divides the hypotenuse into 12mm and 16mm segments. Find the lengths of each of the following. A. The altitude to the hypotenuse B. The shorter leg of angle ABC C. The longer leg … 
Math
the altitude, AD, to the hypotenuse BC of right triangle ABC divides the hypotenuse into segments that are 8 and 10 cm long. find the length of the altitude. 
Geometry
The length of a hypotenuse of a right triangle is 29 feet. The Altitude drawn perpendicular to the hypotenuse is 10 feet. What are the lengths of the two legs? 
Geometry
I need help in this problem: A 14foot ladder is leaning against a house so that its top touches the top of the wall. the bottom of the ladder is 8 feet away from the wall. which of these can be used to find the height of the wall? 
Geometry
The altitude to the hypotenuse of a right triangle divides the hypotenuse into segments 6 inch and 10 inch long, Find the length h of the altitude.