Question

LM is the midsegment of ABCD. AB = x + 8, LM = 4x + 3, and DC = 299. What is the value of x?

Answer 1

The value of x is 43

Step-by-step explanation:

The length of the mid-segment of a trapezoid is the average of the

lengths of its two parallel bases

→ Mid-segment = $\frac{base_{1}+base_{2}}{2}$

∵ ABCD is a trapezoid, where AB // CD

∵ LM is the mid-segment

∴ LM = $\frac{AB+CD}{2}$

∵ LM = 4 x + 3

∵ AB = x + 8

∵ CD = 299

Substitute these values in the rule above

∴ (4 x + 3) = $\frac{(x + 8)+299}{2}$

∴ (4 x + 3) = $\frac{(x + 307}{2}$

- Multiply both sides by 2

∴ 2(4 x + 3) = x + 307

- Multiply the bracket by 2

∴ 8 x + 6 = x + 307

- Subtract x from both sides

∴ 7 x + 6 = 307

- Subtract 6 from both sides

∴ 7 x = 301

- Divide both sides by 7

∴ x = 43

The value of x is 43

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