Question

lesson 5: quadrilaterals
congruent and similar polygons
which of the following is similar to a rectangle with a length of 16 cm and width of 10 cm?
a. rectangle with a length of 32 cm and a width of 8 cm
b. rectangle with a length of 5 cm and a width of 8 cm
c. rectangle with a length of 16 cm and a width of 9 cm
d. rectangle with a length of 8 cm and a width of 4 cm
check answer

Explanation:

Step1: Recall similarity ratio formula

For two rectangles to be similar, the ratios of their corresponding sides must be equal. Let the first rectangle have length $l_1 = 16$ cm and width $w_1=10$ cm. For a second rectangle with length $l_2$ and width $w_2$, we need $\frac{l_1}{w_1}=\frac{l_2}{w_2}$. The ratio of the sides of the given rectangle is $\frac{l_1}{w_1}=\frac{16}{10}=\frac{8}{5}=1.6$.

Step2: Check option a

For a rectangle with $l_2 = 32$ cm and $w_2 = 8$ cm, the ratio $\frac{l_2}{w_2}=\frac{32}{8}=4
eq1.6$.

Step3: Check option b

For a rectangle with $l_2 = 5$ cm and $w_2 = 8$ cm, the ratio $\frac{l_2}{w_2}=\frac{5}{8}=0.625
eq1.6$.

Step4: Check option c

For a rectangle with $l_2 = 16$ cm and $w_2 = 9$ cm, the ratio $\frac{l_2}{w_2}=\frac{16}{9}\approx1.78
eq1.6$.

Step5: Check option d

For a rectangle with $l_2 = 8$ cm and $w_2 = 4$ cm, the ratio $\frac{l_2}{w_2}=\frac{8}{4}=2
eq1.6$.
Since none of the given rectangles have the same ratio of length - to - width as the rectangle with length 16 cm and width 10 cm, there is an error in the problem setup or options. If we assume the intended ratio calculation is considered in a different order or there is a mis - type, re - evaluating the ratios in a more lenient way (allowing for $\frac{l_1}{w_1}=\frac{w_2}{l_2}$ or vice - versa in some cases which is incorrect for strict similarity but for the sake of finding the 'closest' in a wrong - option scenario):
Let's re - check the ratios considering all possible comparisons.
For the original rectangle ratio of sides is $\frac{16}{10} = 1.6$.
For option a: $\frac{32}{8}=4$, $\frac{8}{32}=0.25$.
For option b: $\frac{5}{8}=0.625$, $\frac{8}{5} = 1.6$. This rectangle has the ratio of sides equal to the reciprocal of the ratio of the sides of the given rectangle. In the context of similarity of rectangles, if we consider the ratio of corresponding sides (even if we swap length and width in the comparison), rectangle b has a side - ratio relationship that can be considered in a non - standard but related way.

Answer:

b. Rectangle with a length of 5 cm and a width of 8 cm