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For triangle ABC use the Triangle Proportionality Theorem to solve for x

1. what is the value of x?

2. What is the perimeter of triangle ABC?

show ALL work-- PLEASE HELP!

For triangle ABC use the Triangle Proportionality Theorem to solve for x 1 what is the value of x 2 What is the perimeter of triangle ABC show ALL work PLEASE H class=

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DᴀʀᴋPᴀʀᴀᴅᴏx

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Here's the solution ~

The two triangles in the shown figure are similar, therefore conclusion can be made that :

Ratio of its it's corresponding sides is equal.

[tex]\qquad \sf  \dashrightarrow \: \dfrac{2x - 4 + 6}{6} = \dfrac{24}{4} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{2x + 2}{6} = 6[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2x + 2 = 6 \times 6[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2x + 2 = 36[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2x = 36 - 2[/tex]

[tex]\qquad \sf  \dashrightarrow \: 2x = 34[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 17[/tex]

Therefore, The value of x is " 17 "

Now, the measure of side BC is :

[tex]\qquad \sf  \dashrightarrow \: 2x - 4[/tex]

[tex]\qquad \sf  \dashrightarrow \:2 (17) - 4[/tex]

[tex]\qquad \sf  \dashrightarrow \: 34 - 4[/tex]

[tex]\qquad \sf  \dashrightarrow \: 30 \: \: units[/tex]

So, its perimeter will be :

[tex]\qquad \sf  \dashrightarrow \: p = AB + AB + BC [/tex]

[tex]\qquad \sf  \dashrightarrow \: p = 24 + 26 + 30[/tex]

[tex]\qquad \sf  \dashrightarrow \: p = 80 \: \: units[/tex]

mhanifa

Answer:

  • 1) x = 17,
  • 2) P = 86 units.

------------------------------------

Part 1

According to Triangle Proportionality Theorem we have the following equal proportions:

  • (24 - 4)/4 = (2x - 4)/6
  • 20/4 = (x - 2)/3
  • 5 = (x - 2)/3
  • x - 2 = 5*3
  • x - 2 = 15
  • x = 17

Part 2

The missing side is:

  • BC = 6 + 5*6 = 6 + 30 = 36 units

The perimeter is:

  • P = 24 + 36 + 26 = 86 units

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