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Please see the image below(math)

Please see the image below(math)-example-1
User James Buck
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2 Answers

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Answer:

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.

User Tamarisk
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2 votes

Answer:

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

User Colm Prunty
by
7.5k points

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