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3 years ago

The diagram shows corresponding lengths in two similar figures. Find the area of the smaller figure.

Mathematics

2 answers:

nikitadnepr [17]3 years ago

7 0

Answer:

Correct choice is D

Step-by-step explanation:

If two similar figures have the coefficient of similarity k, then the ratio between the area of these figures is equal to $k^2.$

You are given corresponding lengths in two similar figures, then

$k=\dfrac{15}{20}=\dfrac{3}{4}.$

Therefore,

$\dfrac{A_{small}}{A_{large}}=\left(\dfrac{3}{4}\right)^2=\dfrac{9}{16}$

and

$A_{small}=\dfrac{9}{16}\cdot A_{large}=\dfrac{9}{16}\cdot 64=9\cdot 4=36\ cm^2.$

butalik [34]3 years ago

5 0

The area are in the ratio of the squares of corresponding sides.

That is 15^2 : 20^2 = 225:400

so the area of the smaller figure = (225/400) * 64

= 0.5625 * 64

= 36 cm^2 (answer)

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The proportion of the recipe required to make the grocery list is obtained from the recipe for the beans soup.

The grocery list is therefore;

15 cups of honey beans

9 cups carrots

12 cups cherry tomato

192 oz. vegetable broth

10.5 cup turnips

6 teaspoon salt

8 cups potato onions

1.25 teaspoons thyme

12 teaspoons garlic

Reason:

Amounts of beans soup Sam wants to make = 4 gallons

The recipe for the beans soup is as follows as obtained from an online home work document are;

Vegetable Bean Soup that Serves 4 with volume of 0. $\overline 3$ gallons

1.25 cups of honey beans

0.75 cup carrots

1 cup cherry tomato

16 oz. vegetable broth

0.875 cup turnips

0.5 teaspoon salt

$0.\overline 6$ cup potato onions

0.125 teaspoon thyme

1 teaspoon garlic

The amount of each ingredient Sam needs is given by the ratio of amount of soup Sam wants to make and the given amount of soup made by the ingredients as follows;

$Multiple \ of \ ingredient \ amount = \dfrac{4}{0. \overline 3} = \dfrac{4}{\dfrac{1}{3} } = 4 \times 3 = 12$

Therefore, Sam has to buy twelve times the amount of each ingredient as follows;

Vegetable Bean Soup that Serves 4 with volume of 0. $\mathbf{\overline 3}$ gallons

12 × 1.25 = 15 cups of honey beans

12 × 0.75 = 9 cups of carrots

12 × 1 = 12 cups of cherry tomato

12 × 16 = 192 oz. vegetable broth

12 × 0.875 = 10.5 cup turnips

12 × 0.5 = 6 teaspoon salt

12 × $0.\overline 6$ = 8 cups of potato onions

12 × 0.125 = 1.25 teaspoons thyme

12 × 1 = 12 teaspoons garlic

The grocery list is therefore;

15 cups of honey beans

9 cups carrots

12 cups cherry tomato

192 oz. vegetable broth

10.5 cup turnips

6 teaspoon salt

8 cups potato onions

1.25 teaspoons thyme

12 teaspoons garlic

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