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The formula is D=w2+l2{\displaystyle D={\sqrt {w^{2}+l^{2}}}}, where D{\displaystyle D} equals the length of the rectangle’s diagonal, l{\displaystyle l} equals the length of the rectangle, and w{\displaystyle w} equals the width of the rectangle.  This method will only work if you are given the length of the diagonal and the length of the side of the rectangle. You might also see the formula written as D=w2+h2{\displaystyle D={\sqrt {w^{2}+h^{2}}}}, where h{\displaystyle h} equals the height of the rectangle and is used instead of length. The variables l{\displaystyle l} and h{\displaystyle h} refer to the same measurement. Make sure you substitute for the correct variables. For example, if you are trying to find the width of a rectangle that has a diagonal length of 5 centimeters, and a side length of 4 centimeters, your formula will look like this: 5=w2+42{\displaystyle 5={\sqrt {w^{2}+4^{2}}}} You need to do this to get rid of the square root sign, which makes isolating the width variable easier. For example:5=w2+42{\displaystyle 5={\sqrt {w^{2}+4^{2}}}}52=w2+42{\displaystyle 5^{2}=w^{2}+4^{2}}25=w2+16{\displaystyle 25=w^{2}+16} To do this, you need to subtract the squared length from each side of the equation. For example, in the equation 25=16+w2{\displaystyle 25=16+w^{2}}, you would subtract 16 from each side.25=16+w2{\displaystyle 25=16+w^{2}}9=w2{\displaystyle 9=w^{2}} To do this, you need to find the square root of each side of the equation. For example:9=w2{\displaystyle {\sqrt {9}}={\sqrt {w^{2}}}}3=w{\displaystyle 3=w} Don’t forget to include the unit of measurement. For example, for a rectangle with a diagonal length of 5cm{\displaystyle 5cm} and a side length of 4cm{\displaystyle 4cm}, the width would be 3cm{\displaystyle 3cm}.
Set up the formula for the diagonal of a rectangle. Plug the values for the diagonal and side length into the formula. Square both sides of the formula. Isolate the w{\displaystyle w} variable. Solve for w{\displaystyle w}. Write your final answer.