Consider that the length of rectangle A is 10 cm and its width is 6 cm. Which rectangle is similar to rectangle A? A) A rectangle with a length of 9 cm and a width of 6 cm. B) A rectangle with a length of 15 cm and a width of 9 cm. C) A rectangle with a length of 14 cm and a width of 7 cm. D) A rectangle with a length of 12 cm and a width of 8 cm.

ANSWER

B) A rectangle with a length of 15 cm and a width of 9 cm.

EXPLANATION

The given rectangle, A, has length, 10cm and its width is 6cm.

The rectangle that is similar to rectangle A, has the corresponding sides in the same proportion.

For option A, the triangle has length 9cm and width 6cm.

The ratio of the corresponding sides are:

[tex] \frac{10}{9} \ne \frac{6}{6} [/tex]

Since the ratios are not equal, the two triangles are not similar.

For the triangle in option B, the length is 15cm and the width is 9cm.

The ratio of the corresponding sides are:

[tex] \frac{10}{15} = \frac{6}{9} = \frac{2}{3} [/tex]

Since the sides of the triangle are in the same proportion, the two triangles are similar.

For option C, the proportions are not the same.

[tex] \frac{10}{14} \ne \frac{6}{7} [/tex]

The proportions are not the same for the triangle in option D.

[tex] \frac{10}{12} \ne \frac{6}{8} [/tex]