Two similar triangles have their sides in the ratio 1:3. a. What is the ratio of their respective perimeters? b. If the perimeter of the "larger" triangle is 36x cm, what is the perimeter of the smaller triangle? a. The ratio of their respective perimeters, in reduced terms, is (Type whole numbers.) b. The perimeter of the smaller triangle is cm. (Simplify your answer. Type an exact answer in terms of 1.)
Two similar triangles have their sides in the ratio 1:3. a. What is the ratio of their respective perimeters? b. If the perimeter of the "larger" triangle is 36x cm, what is the perimeter of the smaller triangle? a. The ratio of their respective perimeters, in reduced terms, is (Type whole numbers.) b. The perimeter of the smaller triangle is cm. (Simplify your answer. Type an exact answer in terms of 1.)
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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![### Similar Triangles and Their Perimeters
**Problem Statement:**
Two similar triangles have their sides in the ratio 1:3.
1. **Question a:** What is the ratio of their respective perimeters?
2. **Question b:** If the perimeter of the "larger" triangle is \( 36\pi \) cm, what is the perimeter of the smaller triangle?
**Solution:**
a. The ratio of their respective perimeters, in reduced terms, is \( \boxed{1} : \boxed{3} \).
b. The perimeter of the smaller triangle is \( \boxed{12\pi} \) cm.
(Simplify your answer. Type an exact answer in terms of \( \pi \).)
**Explanation:**
For question a, since the triangles are similar, the ratio of their perimeters is the same as the ratio of their corresponding sides, which is 1:3.
For question b, since the perimeter of the larger triangle is \( 36\pi \) cm, and the ratio of the sides (and thus the perimeters) is 1:3, the perimeter of the smaller triangle can be calculated as follows:
\[ \text{Perimeter of the smaller triangle} = \frac{36\pi}{3} = 12\pi \text{ cm} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdc0b40bc-1527-4d3e-b886-03bf08f02f26%2F20a7bc45-589a-4f5c-8bc0-2752f1d21c70%2Fsvu96aa_processed.png&w=3840&q=75)
Transcribed Image Text:### Similar Triangles and Their Perimeters
**Problem Statement:**
Two similar triangles have their sides in the ratio 1:3.
1. **Question a:** What is the ratio of their respective perimeters?
2. **Question b:** If the perimeter of the "larger" triangle is \( 36\pi \) cm, what is the perimeter of the smaller triangle?
**Solution:**
a. The ratio of their respective perimeters, in reduced terms, is \( \boxed{1} : \boxed{3} \).
b. The perimeter of the smaller triangle is \( \boxed{12\pi} \) cm.
(Simplify your answer. Type an exact answer in terms of \( \pi \).)
**Explanation:**
For question a, since the triangles are similar, the ratio of their perimeters is the same as the ratio of their corresponding sides, which is 1:3.
For question b, since the perimeter of the larger triangle is \( 36\pi \) cm, and the ratio of the sides (and thus the perimeters) is 1:3, the perimeter of the smaller triangle can be calculated as follows:
\[ \text{Perimeter of the smaller triangle} = \frac{36\pi}{3} = 12\pi \text{ cm} \]
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