Two rectangles are similar with a scale factor of . If the area of the larger rectangle is , find the area of the smaller rectangle.
Select one:
a.
b.
c.
d.

Ask by Simpson Mejia. in the United States

Mar 28,2025

Question

Two rectangles are similar with a scale factor of . If the area of the larger rectangle is , find the area of the smaller rectangle.
Select one:
a.
b.
c.
d.

Ask by Simpson Mejia. in the United States

Mar 28,2025

UpStudy AI · Accepted Answer

Let the scale factor for the lengths be $$ \frac{6}{7} $$. Since the rectangles are similar, the ratio of their areas is the square of the scale factor. Thus, the area scale factor is

$$
\left(\frac{6}{7}\right)^2 = \frac{36}{49}.
$$

Let the area of the smaller rectangle be $$ A_{\text{small}} $$ and the area of the larger rectangle be $$ A_{\text{large}} = 308\,\text{in}^2 $$. Then

$$
A_{\text{small}} = A_{\text{large}} \times \frac{36}{49} = 308 \times \frac{36}{49}.
$$

To simplify, note that

$$
308 = 7 \times 44,
$$

so

$$
A_{\text{small}} = (7 \times 44) \times \frac{36}{49} = 44 \times \frac{36}{7} = \frac{44 \times 36}{7}.
$$

Evaluating the multiplication in the numerator:

$$
44 \times 36 = 1584,
$$

thus

$$
A_{\text{small}} = \frac{1584}{7} \approx 226.29\,\text{in}^2.
$$

Therefore, the area of the smaller rectangle is approximately $$226.29\,\text{in}^2$$, which corresponds to option d.
The area of the smaller rectangle is approximately $$226.29\,\text{in}^{2}$$, so the correct answer is d.

Two rectangles are similar with a scale factor of . If the area of the larger rectangle is , find the area of the smaller rectangle.
Select one:
a.
b.
c.
d.

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Two rectangles are similar with a scale factor of . If the area of the larger rectangle is , find the area of the smaller rectangle. Select one: a. b. c. d.

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Two rectangles are similar with a scale factor of . If the area of the larger rectangle is , find the area of the smaller rectangle.
Select one:
a.
b.
c.
d.