Video: Finding the Length of a Rectangle given a Relation between Its Dimensions

π‘Šπ‘‹π‘Œπ‘ is a rectangle where π‘π‘Œ = 9π‘₯ βˆ’ 8 and π‘Šπ‘‹ = 8π‘₯ + 1. Find π‘Šπ‘‹.

02:23

Video Transcript

π‘Šπ‘‹π‘Œπ‘ is a rectangle where π‘π‘Œ is equal to nine π‘₯ minus eight and π‘Šπ‘‹ is equal to eight π‘₯ plus one. Find π‘Šπ‘‹.

So we’ve been told that π‘Šπ‘‹π‘Œπ‘ is a rectangle and asked to find π‘Šπ‘‹ which is the length of one of the sides of the rectangle. We’ve been given an expression for its length in terms of the variable lowercase π‘₯. It is equal to eight π‘₯ plus one. We’ve also been given an expression for the opposite side of the rectangle π‘π‘Œ, which is equal to nine π‘₯ minus eight.

In order to find the length of the side π‘Šπ‘‹, we need to find the value of the variable lowercase π‘₯. Let’s think about how we can use the information we’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‘Š and π‘Œπ‘‹ are equal in length.

But also more usefully, the sides π‘π‘Œ and π‘Šπ‘‹ are equal in length. As we’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 I’ll subtract eight π‘₯ from each side. This gives π‘₯ is equal to nine. So we’ve solved the equation and found the value of π‘₯. Remember, in this question, we’re asked to find the length of the side π‘Šπ‘‹. π‘Šπ‘‹ 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 haven’t been given any units to use in this question, so the length of π‘Šπ‘‹ is 73.

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