   SEARCH HOME Math Central Quandaries & Queries  Question from Mattie, a parent: The dimensions of a rectangular-shaped picture frame are 14 inches long and four inches wide. Which dimensions below represent another frame that is geometrically similar> a. l=49 in. and w=14in. b. l=7in and w=3in c. l=21in and w=8in d. l=24in and w=14in thanks Hi Mattie,

Two figures are said to be similar when all corresponding angles are equal and all distances are increased (or decreased) in the same ratio.1 Your figures are all rectangles so all the angles are right angles.Thus if you have a rectangle that is 12 inches by 8 inches it is similar to one that is 24 inches by 16 inches (I multiplied the lengths by 2), and similar to one that is 36 inched by 24 inches (I multiplied the lengths by 3), and similar to one that is 6 inches by 4 inches (I multiplied the lengths by $\frac12$).

You are starting with a rectangle that is 14 inches by 4 inches so it is similar to one that is 7 inches by 2 inches. Now look at the options a, b, c and d one at a time. For example for option c if you multiply 7 by 3 you get 21 but multiplying 2 by 3 gives 6 not 8 so c is not he correct answer.

Try the others,
Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.