Question 696621: divide a right angled triangle of sides ab=77 feet is the base,bc=60 feet and ca=97 feet into four equal parts longitudinally.
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! A triangle of sides AB=77 feet, BC=60 feet and CA=97 feet, does not have a right angle at B.
A triangle of sides AB=77 feet, BC=59 feet and CA=97 feet, has an angle at C that is for practical purposes a right angle (not exactly, but you would not notice the difference).
 We need to get  with
AXP and ABC are similar right triangles.
PA and CA are the corresponding longest sides of each triangle;
XP and BC are the corresponding shortest sides, and]=
AX and AB are corresponding sides too.
In similar triangles, the ratio of the areas equals the ratio of the lengths of the corresponding sides, squared.
In math equation: 
So  <-->  <--> 
means  <-->  or
 <--> 
So, if AB=77 feet,  ft -->  ft
If you look hard enough you will see that there are 4  right triangles with a vertex at A:
ABC, AZR, AYQ, and AXP.
How are their areas related?
ABC is split into its 4 pieces of area equal to the area of AXP.
AYQ contains 2 of those pieces, and AZR contains 3.
So  <--> 
and  <--> 
Using again the fact that the ratio of areas equals the ratio of the lengths of the corresponding sides, squared,
 -->  -->  -->  = about  feet
 -->  -->  -->  = about  feet
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