Question Video: Finding the Length of a Rectangle given a Relation between Its Dimensions Mathematics • 8th Grade

ππππ is a rectangle where ππ = 9π₯ β 8 and ππ = 8π₯ + 1. Find ππ.

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Video Transcript

ππππ is a rectangle where ππ is equal to nine π₯ minus eight and ππ is equal to eight π₯ plus one. Find ππ.

So weβve been told that ππππ is a rectangle and asked to find ππ which is the length of one of the sides of the rectangle. Weβve been given an expression for its length in terms of the variable lowercase π₯. It is equal to eight π₯ plus one. Weβve also been given an expression for the opposite side of the rectangle ππ, which is equal to nine π₯ minus eight.

In order to find the length of the side ππ, we need to find the value of the variable lowercase π₯. Letβs think about how we can use the information weβve been given to do this. Well, a key fact about rectangles is that opposite sides are equal in length. For our rectangle, this means that ππ and ππ are equal in length.

But also more usefully, the sides ππ and ππ are equal in length. As weβve 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. We can now solve this equation in order to find the value of the variable π₯. First we add eight to each side of the equation, giving nine π₯ is equal to eight π₯ plus nine.

Next, I want to group all of the π₯ terms on the same side of the equation. So Iβll subtract eight π₯ from each side. This gives π₯ is equal to nine. So weβve solved the equation and found the value of π₯. Remember, in this question, weβre asked to find the length of the side ππ. ππ is equal to eight π₯ plus one. So we need to substitute the value that we have calculated four π₯ into this expression.

This gives eight multiplied by nine plus one. Eight multiplied by nine is 72, and adding one gives 73. We havenβt been given any units to use in this question, so the length of ππ is 73.