Two similar triangles have a scale factor of . If the area of the smaller triangle is 180 cm?, then what is the area of the larger triangle? O 214 cm2 O 480 cm2 150 cm2
Two similar triangles have a scale factor of . If the area of the smaller triangle is 180 cm?, then what is the area of the larger triangle? O 214 cm2 O 480 cm2 150 cm2
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Two similar
![### Geometry Problem on Similar Triangles
**Question:**
Two similar triangles have a scale factor of \(\frac{3}{2}\). If the area of the smaller triangle is 180 cm², then what is the area of the larger triangle?
1. 214 cm²
2. 480 cm²
3. 150 cm²
**Explanation:**
The areas of similar triangles are proportional to the square of the scale factor. Therefore, if the scale factor between the triangles is \(\frac{3}{2}\), the ratio of their areas is \(\left(\frac{3}{2}\right)^2 = \frac{9}{4}\).
To find the area of the larger triangle:
\[
\text{Area of larger triangle} = \text{Area of smaller triangle} \times \frac{9}{4}
= 180 \, \text{cm}^2 \times \frac{9}{4}
= 180 \, \text{cm}^2 \times 2.25
= 405 \, \text{cm}^2
\]
The area of the larger triangle should be among the options given. However, based on the options provided, there appears to be an error as none match the expected calculation. Would need more context or correct choices to make sense of this.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F870e2c1d-d022-4f41-b5d2-13ea4c5e7ced%2Fd4b37d99-8f65-41e7-9750-cf50ec570546%2Fsnmu9t.jpeg&w=3840&q=75)
Transcribed Image Text:### Geometry Problem on Similar Triangles
**Question:**
Two similar triangles have a scale factor of \(\frac{3}{2}\). If the area of the smaller triangle is 180 cm², then what is the area of the larger triangle?
1. 214 cm²
2. 480 cm²
3. 150 cm²
**Explanation:**
The areas of similar triangles are proportional to the square of the scale factor. Therefore, if the scale factor between the triangles is \(\frac{3}{2}\), the ratio of their areas is \(\left(\frac{3}{2}\right)^2 = \frac{9}{4}\).
To find the area of the larger triangle:
\[
\text{Area of larger triangle} = \text{Area of smaller triangle} \times \frac{9}{4}
= 180 \, \text{cm}^2 \times \frac{9}{4}
= 180 \, \text{cm}^2 \times 2.25
= 405 \, \text{cm}^2
\]
The area of the larger triangle should be among the options given. However, based on the options provided, there appears to be an error as none match the expected calculation. Would need more context or correct choices to make sense of this.
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