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Using Algebra in Geometry Study Guide (page 2)

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Updated on Oct 3, 2011

Example

If the length of one side of a square is (x + 8) units, what is the area of the square in terms of x?

The formula for area of a square is Asquare = s2, so we must square the length of one side of the square: (x + 8)2 = (x + 8)(x + 8). Use FOIL to find the area of the square:

      First: (x)(x) = x2
      Outside: (x)(8) = 8x
      Inside: (8)(x) = 8x
      Last: (8)(8) = 64
      x2 + 8x + 8x + 64 = x2 + 16x + 64.

The area of the square is x2 + 16x + 64 square units.

Example

The height of a cone is twice its radius. If the volume of the cone is 18π cm3, what is the height of the cone?

Let x equal the radius of the cone. Because the height of the cone is twice the radius, the height is 2x. The formula for volume of a cone is Vcone = πr2h, so substitute 18π for V, x for r, and 2x for h:

      27 = x3
      3 = x

The radius is 3 centimeters. Because the height is twice the radius, the height of the cone is 6 centimeters.

Find practice problems and solutions for these concepts at Using Algebra in Geometry Practice Questions.

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