Question

Rectangle A has length 12 and width 8. Rectangle B has length 15 and width 10. Rectangle C has length 30 and width 15. Is Rectangle A a scaled copy of Rectangle B? If so, what is the scale factor? Is Rectangle B a scaled copy of Rectangle A? If so, what is the scale factor? Explain how you know that Rectangle C is not a scaled copy of Rectangle B. Is Rectangle A a scaled copy of Rectangle C? If so, what is the scale fact

Answer 1

Rectangles are similar figures, thus if scaled copies of each other then the ratios of corresponding sides must be equal

compare ratios of lengths and widths

rectangles A and B

k = $\frac{12}{15}$ = $\frac{4}{5}$ ← ratio of lengths

k = $\frac{8}{10}$ = $\frac{4}{5}$ ← ratio of widths

scale factors are equivalent, hence rectangle A is a scaled copy of B

rectangles C and B

k = $\frac{15}{30}$ = $\frac{1}{2}$ ← ratio of lengths

k = $\frac{10}{15}$ = $\frac{2}{3}$ ← ratio of width

scale factors (k ) are not equal, hence C is not a scaled copy of B

rectangles A and C

k = $\frac{30}{12}$ = $\frac{5}{2}$ ← ratio of lengths

k = $\frac{15}{8}$ ← ratio of widths

the scale factors are not equal hence A is not a scaled copy of C