The area of an equilateral triangle with sides of length x is given by the function √3 defined by A(x) = 4 X X A(8x)= (Type an exact answer.) A(40)= (Type an exact answer.) CID (a) Find A(8x), the function representing the area of an equilateral triangle with sides of length eight times the original length. (b) Find the area of an equilateral triangle with side length 40. Use your formula for A(8x) found in part (a).
The area of an equilateral triangle with sides of length x is given by the function √3 defined by A(x) = 4 X X A(8x)= (Type an exact answer.) A(40)= (Type an exact answer.) CID (a) Find A(8x), the function representing the area of an equilateral triangle with sides of length eight times the original length. (b) Find the area of an equilateral triangle with side length 40. Use your formula for A(8x) found in part (a).
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Equilateral Triangle Area Calculation**
The area of an equilateral triangle with sides of length \( x \) is given by the function defined by \( A(x)= \frac{\sqrt{3}}{4}x^2 \).
### Tasks:
**(a)** Find \( A(8x) \), the function representing the area of an equilateral triangle with sides of length eight times the original length.
**(b)** Find the area of an equilateral triangle with side length 40. Use your formula for \( A(8x) \) found in part (a).
#### Given Equation:
\[ A(x) = \frac{\sqrt{3}}{4} x^2 \]
**Diagram:**
The diagram present in the image shows an equilateral triangle with each side labeled \( x \).
### Solution Steps:
**Part (a): Finding \( A(8x) \):**
1. Start with the original area function: \( A(x) = \frac{\sqrt{3}}{4} x^2 \).
2. Substitute \( 8x \) into the function in place of \( x \):
\[
A(8x) = \frac{\sqrt{3}}{4} (8x)^2
\]
**Part (b): Finding the area for side length 40:**
1. Given side length \( x = 40 \).
2. Substitute \( x = 40 \) into the appropriate area formula found in part (a).
**Answer Fields:**
- \( A(8x) = \) (Type an exact answer.)
- \( A(40) = \) (Type an exact answer.)
**Note:** Ensure to substitute correctly and simplify wherever necessary.
**Example:**
If the function found in part (a) simplifies to a particular expression, follow through with that simplified formula for accurate results in part (b).
**Time Remaining: 00:39:53**
**Next: Click the 'Next' button to proceed after filling the answers.**
This comprehensive approach ensures clear understanding and accurate solutions in calculating the area of equilateral triangles when sides are scaled.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F87bb6fa2-16f6-449b-8672-e576ef2a7d16%2F21b28ac7-1c84-4da3-accb-c2ff9dbea922%2F1hei8ng_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Equilateral Triangle Area Calculation**
The area of an equilateral triangle with sides of length \( x \) is given by the function defined by \( A(x)= \frac{\sqrt{3}}{4}x^2 \).
### Tasks:
**(a)** Find \( A(8x) \), the function representing the area of an equilateral triangle with sides of length eight times the original length.
**(b)** Find the area of an equilateral triangle with side length 40. Use your formula for \( A(8x) \) found in part (a).
#### Given Equation:
\[ A(x) = \frac{\sqrt{3}}{4} x^2 \]
**Diagram:**
The diagram present in the image shows an equilateral triangle with each side labeled \( x \).
### Solution Steps:
**Part (a): Finding \( A(8x) \):**
1. Start with the original area function: \( A(x) = \frac{\sqrt{3}}{4} x^2 \).
2. Substitute \( 8x \) into the function in place of \( x \):
\[
A(8x) = \frac{\sqrt{3}}{4} (8x)^2
\]
**Part (b): Finding the area for side length 40:**
1. Given side length \( x = 40 \).
2. Substitute \( x = 40 \) into the appropriate area formula found in part (a).
**Answer Fields:**
- \( A(8x) = \) (Type an exact answer.)
- \( A(40) = \) (Type an exact answer.)
**Note:** Ensure to substitute correctly and simplify wherever necessary.
**Example:**
If the function found in part (a) simplifies to a particular expression, follow through with that simplified formula for accurate results in part (b).
**Time Remaining: 00:39:53**
**Next: Click the 'Next' button to proceed after filling the answers.**
This comprehensive approach ensures clear understanding and accurate solutions in calculating the area of equilateral triangles when sides are scaled.
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