Video: Creating Quadratic Equations with One Variable

The length of a rectangle is 3 cm more than double the width. The area of rectangle is 27 cm². Write an equation that can be used to find 𝑤, the width of the rectangle, in centimeters.

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Video Transcript

The length of a rectangle is three centimetres more than double the width. The area of the rectangle is 27 centimetres squared. Write an equation that can be used to find 𝑤, the width of the rectangle, in centimetres.

Here’s our rectangle. It has a width that we don’t know. We also don’t know the length. But we do know some information about the length. The length is three more than double the width. We can write double the width as two 𝑤. So we can say that the length equals two 𝑤 plus three.

The area of this rectangle is 27 centimetres squared. We know that the area of rectangles can be found by multiplying the length times the width. We know the area is 27. 27 must equal the length, two 𝑤 plus three, times the width, 𝑤. By solving this equation, 27 equals two 𝑤 plus three times 𝑤, we could find what 𝑤 would equal.

You could also flip the order of the parentheses and have an equally correct equation for solving for 𝑤. You could also say 27 equals 𝑤 times two 𝑤 plus three.

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