Question

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!!

Answer 1

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

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