FOUNDATIONS FOR SUCCESS: CONSULTATION DRAFT
G18. Similar Polygons B Q
A
P D
S R
C
ABCD and PQRS are similar polygons whose perimeters are 40 inches and 30 inches, respectively. The area enclosed by ABCD is 8 square inches. a) What area is enclosed by PQRS? b) Is it possible for the straight-line distance from point A to point C to be 20 inches?
A SOLUTION
a) The perimeter of PQRS is 30, and the perimeter of ABCD is 40. Therefore the ratio of the linear dimensions of the polygons is 3 . So the ratio of the areas of the polygons will be given by the square 4 3 2 9 of the ratio of the linear dimensions, that is, @ 4 # p 16 . So: APQRS p 9 AABCD p 9 x 8 p 9 p 4.5 in2. 16 16 2 b) No. If the distance from A to C were 20, then by the triangle inequality, AD c DC 1 20 and AB c BC 1 20, which would make the perimeter greater than 40.
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