How to Find the Length & Width of a Rectangle When Given the Area

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Rectangles are shapes used in math problems.
Rectangles are shapes used in math problems.

Area and perimeter are two common terms that are used when examining rectangles. The area of a rectangle is the amount of space it takes up and is found by multiplying its length times its width. The perimeter of a rectangle is the sum of the length of all four sides of it. A rectangle has four sides, two of which are the width and two are the length. Both sides of the width are equal and both sides of the length are equal.


    • 1

      Solve for the length and width using the formula: area = length times width (lw). If the area is 32 and the length is twice as long as the width, begin by writing: l = 2w. This means that the length is equal to two times the width.

    • 2

      Fill in the formula. The formula is area = lw. Substitute the 1 = 2w for the l and add in the 32 by writing: 32 = 2w times w. 2w times w equals 2w^2; so the equation reads: 32 = 2w^2.

    • 3

      Divide the sides. Divide both sides by 2 to leave only the w^2 on the right side of the equation and 16 on the other side.

    • 4

      Find the square root. To solve for w, you must divide both sides by the square root. The square root of 16 is 4, so the answer reads: 4 = w. The width therefore is 4.

    • 5

      Solve for the length. If the width is 4 and the length is equal to twice as much as the width, then the length is 8.

    • 6

      Check your answer. Area is equal to length times width. In this example, double check your answer by multiplying 8 times 4. The answer is correct because it is 32.

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