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 = [tex]\frac{base_{1}+base_{2}}{2}[/tex]
∵ ABCD is a trapezoid, where AB // CD
∵ LM is the mid-segment
∴ LM = [tex]\frac{AB+CD}{2}[/tex]
∵ LM = 4 x + 3
∵ AB = x + 8
∵ CD = 299
Substitute these values in the rule above
∴ (4 x + 3) = [tex]\frac{(x + 8)+299}{2}[/tex]
∴ (4 x + 3) = [tex]\frac{(x + 307}{2}[/tex]
- 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
Learn more:
You can learn more about equations in brainly.com/question/10708697
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