WEBVTT
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A shepherd wants to build a rectangular sheep barn.
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The length of the barn must be more than 88 meters, and its perimeter must be less than 253 meters.
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Derive the system of inequalities that describes the situation, denoting the length of the barn by π₯ and its width by π¦.
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Letβs start by highlighting what we know.
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The length of the barn is represented by π₯.
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The width of the barn is represented by π¦.
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We know that the length of the barn must be more than 88 meters.
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We can translate that into an inequality that says π₯ must be greater than 88 meters.
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The barnβs perimeter must be less than 253 meters.
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Perimeter must be less than 253 meters.
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What is the formula for finding the perimeter of a rectangle?
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Usually, we write the formula like this: two times the length plus the width.
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But our instructions gave us variables that we should use for the length and the width.
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Instead of π for the length, we should put in π₯.
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Instead of π€ for the width, weβll include π¦.
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This inequality would then read: two times π₯ plus π¦ must be less than 253 meters.
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Here are two inequalities that describe the situation of the shepherd and his sheep barn.