Final answer:
To find the side length of the smaller equilateral triangle, we can use an algebraic equation, 3(x + 1.05) = 9.83, or a straightforward subtraction and division method. In both cases, we determine that the side length of the smaller triangle is approximately 2.23 m.
Step-by-step explanation:
The student is asked to determine the side length of the smaller triangle when two equilateral triangles differ in their side lengths by 1.05 m, and the perimeter of the larger triangle is 9.83 m. We can address part a) by setting up an equation of the form a(x + b) = c, where x is the side length of the smaller triangle, a is 3 (since there are three sides in a triangle), b is the difference in side length between the two triangles (1.05 m), and c is the perimeter of the larger triangle (9.83 m). The equation becomes 3(x + 1.05) = 9.83.
To solve this equation:
- First, distribute the 3 to get 3x + 3.15 = 9.83.
- Next, subtract 3.15 from both sides to get 3x = 6.68.
- Finally, divide both sides by 3 to get x = 2.2267 m as the side length of the smaller triangle.
For part b), a different method is to subtract the total difference in the perimeters from the perimeter of the larger triangle to get the perimeter of the smaller triangle, and then divide by 3 to find the side length. The total difference in perimeters is 3 * 1.05 = 3.15 m. So, the perimeter of the smaller triangle is 9.83 m - 3.15 m = 6.68 m. To find the side length of the smaller triangle, divide the perimeter by 3: 6.68 m ÷ 3 = 2.2267 m.
Both methods result in the same answer, confirming that the side length of the smaller triangle is approximately 2.23 m (to two decimal places).