SOLUTION: There is a triangle with two lines drawn from hypotenuse to longest leg, creating three similar triangles, each one is a right triangle. You are told that the two line segments (

Algebra ->  Triangles -> SOLUTION: There is a triangle with two lines drawn from hypotenuse to longest leg, creating three similar triangles, each one is a right triangle. You are told that the two line segments (      Log On


   

Question 494949: There is a triangle with two lines drawn from hypotenuse to longest leg, creating three similar triangles, each one is a right triangle. You are told that the two line segments (drawn on the inside of the triangle) create 3 lines of equal size (on the side of the hypotenuse of largest triangle) Then you are told that the area of the smallest triangle is 42 and asked to find the area of the largest triangle. (you are not given any lengths)
Answer by cleomenius(959) About Me  (Show Source):
You can put this solution on YOUR website!
The triangles are proportional since they are similiar
The middle triangle should be in 2:1 proportion from the smaller, since the segments along the hypotenuse are in a two to one ratio.
Since we multiply the length times height, each in a 2 to ratio, we would multiply the Area of the smaller triangle * 4.(2 * 2)
The larger trianlge is in a 3 to 1 ratio over the smaller triangle; since we have two sides we would multiply the area of the smaller triangle by 9 (3*3) to obtain 756.
Cleomenius.