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ππππ is a rectangle where ππ is equal to nine π₯ minus eight and ππ is equal to eight π₯ plus one.
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Find ππ.
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So weβve been told that ππππ is a rectangle and asked to find ππ which is the length of one of the sides of the rectangle.
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Weβve been given an expression for its length in terms of the variable lowercase π₯.
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It is equal to eight π₯ plus one.
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Weβve also been given an expression for the opposite side of the rectangle ππ, which is equal to nine π₯ minus eight.
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In order to find the length of the side ππ, we need to find the value of the variable lowercase π₯.
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Letβs think about how we can use the information weβve been given to do this.
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Well, a key fact about rectangles is that opposite sides are equal in length.
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For our rectangle, this means that ππ and ππ are equal in length.
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But also more usefully, the sides ππ and ππ are equal in length.
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As weβve been given expressions for the lengths of these two sides, we can equate them, giving the equation nine π₯ minus eight is equal to eight π₯ plus one.
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We can now solve this equation in order to find the value of the variable π₯.
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First we add eight to each side of the equation, giving nine π₯ is equal to eight π₯ plus nine.
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Next, I want to group all of the π₯ terms on the same side of the equation.
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So Iβll subtract eight π₯ from each side.
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This gives π₯ is equal to nine.
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So weβve solved the equation and found the value of π₯.
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Remember, in this question, weβre asked to find the length of the side ππ.
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ππ is equal to eight π₯ plus one.
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So we need to substitute the value that we have calculated four π₯ into this expression.
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This gives eight multiplied by nine plus one.
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Eight multiplied by nine is 72, and adding one gives 73.
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We havenβt been given any units to use in this question, so the length of ππ is 73.