LM is the midsegment of trapezoid ABCD. AB= x + 8, LM = 4x + 3, and DC = 187. What is the value of x?

2 ∣ D C ∣ + ∣ A B ∣ ​ = ∣ L M ∣ ∣ A B ∣ = x + 8 ; ∣ L M ∣ = 4 x + 3 ; ∣ D C ∣ = 187 s u b s t i t u t e : 2 187 + x + 8 ​ = 4 x + 3 / ⋅ 2 195 + x = 8 x + 6 / − 195 ; / − 8 x − 7 x = − 189 / : 7 x = 27 ​ ​

Answered by Anonymous | 2024-06-24

To find the value of x in trapezoid ABCD where LM is the midsegment, we used the formula L M = 2 A B + D C ​ . By substituting the given expressions and simplifying, we found that the value of x is 27. Thus, the lengths were verified by solving the equation step-by-step.
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Answered by Anonymous | 2024-12-20