Victory for the ACT Student Text 15e

L ESSON 4 | G EOMETRY • 239

If the width of a rectangle is increased by 10% and the length of the rectangle is increased by 20%, by what percentage does the area of the rectangle increase ? F. 2% G. 10% H. 15% J. 32% K. 36%

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Throwback to Math Class 1. The radius of a circle is equal to one-half of the diameter : r d 2 . 2. The circumference of a circle is equal to the diameter multiplied by r : circumference 2 d r r r . 3. The area of a circle is equal to the radius squared multiplied by r : area r r circle 2 . Š‡ ϐ‹‰—”‡ „‡Ž‘™ •Š‘™• –™‘ ’—ŽŽ‡›• connected by a belt. If the centers of the pulleys are 8 feet apart and the pulleys each have a radius of 1 foot, what is the length, in feet, of the belt? A. 4 r B. 8 r C. 8 r D. 16 r E. 16 2 r Throwback to Math Class 1. The diagonal of a rectangle is the hypotenuse of a right triangle with legs that are the length and width of the rectangle. 2. The perimeter of a rectangle is equal to the sum of the lengths of the four sides: w l 2 2 perimeter = + . s s s s 1 2 3 4 rectangle + + + = of a rectangle is equal to the length multiplied by the width: ar a rectangle lw . 3. The area

CIRCLES

If the area of a circle is equal to 9 r , which of the following is (are) true? I. The radius is 3. II. The diameter is 6. III. The circumference is 6 r . A. I only B. II only C. III only D. I and II only E. I, II, and III  –Š‡ ϐ‹‰—”‡ „‡Ž‘™ǡ O is the center of the circle, and PQ is tangent to the circle at P . If the radius of circle O has a length of 6, what is the area of the shaded portion of –Š‡ ϐ‹‰—”‡ǫ

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PROPERTIES OF TANGENT LINES

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F. r G. 3 r H. 6 r J. 9 r K. 12 r