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Solve the following problem, round your answer to the nearest 2 decimal places if needed.
DE is a midsegment of AABC if AC = x + 9 yards and DE = 2x - 3 yards, solve for x.

100pts!!

Solve the following problem round your answer to the nearest 2 decimal places if needed DE is a midsegment of AABC if AC x 9 yards and DE 2x 3 yards solve for x class=

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akposevictor

Applying the midsegment theorem, the value of x = 5

Recall:

  • The midsegment theorem of a triangle states that the length of the mid-segment (DE) which is parallel to the third side (AC), is half the length of the third side AC of triangle BAC.

Thus:

DE = 1/2(AC)

  • Substitute

2x - 3 = 1/2(x + 9)

  • Multiply both sides by 2

2(2x - 3) = x + 9

4x - 6 = x + 9

  • Combine like terms

4x - x = 6 + 9

3x = 15

  • Divide both sides by 3

x = 5

Therefore, applying the midsegment theorem, the value of x = 5

Learn more about the midsegment theorem on:

https://brainly.com/question/7423948

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