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1. Geometry Item 06-04 A person 5 ft 9 in tall casts a 3 ½ -ft shadow, the foot of which lies at the end of the shadow cast by a tree 12 ft away. How tall is the tree? A. 19 5/7 ft C. 21 ½ ft B. 25 13/28 ft D. 23 ft www.upcatreview.com
2. Geometry Item 06-04 It would be helpful if a drawing is done to illustrate the problem: www.upcatreview.com 7/2 3 ½ ft 5 ft 9 in 12 ft h
3. Geometry Item 06-04 Two similar triangles are formed. If the distances are all in feet and the fractions are written as improper fractions, the following figures result: www.upcatreview.com
5. Geometry Item 06-04 Since the corresponding sides of similar triangles are proportional, the equation of the problem shall be as follows: h : 23/4 = 12 : 7/2 www.upcatreview.com
6. Geometry Item 06-04 Using the Means-Extremes Products Theorem , the equation becomes: (7/2)h = 12(23/4) www.upcatreview.com
7. Geometry Item 06-04 To solve for h, multiply both sides by 2/7: (2/7)(7/2)h = (2/7)(12)(23/4) h = 138/7 ft or 19 5/7 ft ( choice letter A ) www.upcatreview.com
