Question

Please see the image below(math)

Answer 1

y = 21

Explanation:

According to the Side Splitter Theorem, if a line parallel to one side of a triangle intersects the other two sides, then this line divides those two sides proportionally.

Therefore, according to the Side Splitter Theorem:

`\boxed{\sf AD : DB = AH : HC}`

From inspection of the given triangle, the lengths of the line segments are:

• AD = 3
• DB = 7
• AH = 9
• HC = y

To find the value of y, substitute the given line segment lengths into the proportion and solve for y:

`\begin{aligned}\sf AD : DB &=\sf AH : HC\\\\3:7&=9:y\\\\(3)/(7)&=(9)/(y)\\\\3 \cdot y&=9 \cdot 7\\\\3y&=63\\\\(3y)/(3)&=(63)/(3)\\\\y&=21\end{aligned}`

Therefore, the value of y is 21.

Answer 2

21

Explanation:

If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.

AD AH

----- = ---------

AB AH +y

3 9

---- = ------

10 9+y

Using cross products:

3(9+y) = 9*10

27+3y = 90

3y = 90-27

3y =63

y = 63/3

y = 21