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Arterial walls are actually thicker to cope with the high pressure. It is easier for a thin-walled vessel to rupture than a thick-walled vessel. 

In veins, because there is no pressure, blood has to be able to flow back fairly rapidly to be used again. Because of this, veins have larger lumens to allow blood to pass more quickly when not under pressure.
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Arteries carry blood away from the heart and veins return blood to the heart. Veins are generally larger in diameter, carry more blood volume and have thinner walls in proportion to their lumen. Arteries are smaller, have thicker walls in proportion to their lumen and carry blood under higher pressure than veins
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