The area of a rectangle is 65 m2, and the length of the rectangle is 3 m less than twice the width. Find the dimensions of the rectangle?


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Taylor Brookes answered

The area of a rectangle is just the width multiplied by the length, so to solve this problem, you need to find out what the width is and what the length is.

You know that the length (L) is twice the width (W) minus three, which can be written like this: L = 2W - 3

The whole area (which is 65) is the length (2W - 3) multiplied by the width (W) which can be written as: W(2W - 3) = 65

This can be expanded to 2(Wsquared) - 3W = 65

If you take away 65 from both sides you get: 2(Wsquared) - 3W - 65 = 0  -This is called a quadratic.

You then have to use the quadratic formula which will give you two values for W, but the width of a rectangle can't be a negative number, so you want the solution that is positive.

Once you have done this, simply swap out W in the equation L = 2W - 3 for the solution you just found and solve it to find L.

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