Honors Geometry Companion Book, Volume 2

9.2.2 Effects of Changing Dimensions Proportionally (continued) Example 3 Effects of Changing Area The effect of a change in area on the radius of a circle is determined in this example. A circle has a radius of 7 ft. The area of the circle is A = πr 2 = 49 π ft 2 .

Multiplying the area by a factor of 5 gives an area of 245 π . Substitute this value into the formula for area to find the radius of a circle with this area. Solving for r gives r 7 5. = Increasing the area by a factor of 5 has the effect of increasing the radius by a factor of 5. The effect of a change in area on the perimeter of a square is determined in this example. A square has sides of 5 m. The perimeter of the square is 4(5) = 20 m. The area of the square is A = s 2 = 5 2 = 25 m 2 . Multiplying the area by a factor of 3 gives an area of 75 m 2 . Substitute this value into the formula for area to find the length of the side of a square with this area. Solving for s gives s 5 3. = The perimeter of this square is 20 3. Increasing the area by a factor of 3 has the effect of increasing the perimeter by a factor of 3.

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