Answer:
JH=16
Step-by-step explanation:
Hi there!
We are given ΔHIJ, where HI is parallel to KL, and that JK=10, JI=40, and JL=25
We want to find JH
We can use something called the Triangle Proportionality Theorem to help us find JH
The Triangle Proportionality Theorem essentially states that if there is a line parallel to one of the sides of a triangle that intersects the other 2 sides of that triangle, then that segment divides those sides proportionally
In other words, KL is parallel to HI and intersects both HJ and JI, and JK, JH, JL, and JI create a proportion, which is [tex]\frac{JK}{JH} =\frac{JL}{JI}[/tex]
We can substitute the values that we know into that equation
[tex]\frac{10}{JH} =\frac{25}{40}[/tex]
We can simplify 25/40 to 5/8.
[tex]\frac{10}{JH} =\frac{5}{8}[/tex]
Now we can cross multiply (use the means-extreme theorem)
Multiply 10 and 8 together, and set that equal to 5 times JH
80 = 5JH
Divide both sides by 5
16=JH
Hope this helps!
See more on the Triangle Proportionally Theorem here: https://brainly.com/question/20064024
