To answer these questions let's tackle the concept of performing operations on like terms.
When adding like terms, we focus on the parts of the terms that are similar and combine them to simplify the expression.
To add like terms, we follow these steps:
1. Identity-like terms: Look for terms that have the same variables raised to the same powers. For example, 3x, 5x, and -2x are like terms because they all have the variable x raised to the power of 1.
2. Combine the coefficients: Add or subtract the coefficients (the numbers in front of the variables) of the like terms. For example, when adding 3x + 5x - 2x, we combine the coefficients of x, which gives us 6x.
(Keep the variables and exponents unchanged)
3. Combine any constant terms: If there are any constant terms without variables, such as numbers without variables attached, add or subtract them separately. For example, in the expression 2 + 4 + 7, we can combine the constants to get 13.
Now let's answer each question with our new knowledge!
a. For the larger triangle:
Perimeter = (4x + 2) + (7x + 7) + (5x - 4)
= 4x + 2 + 7x + 7 + 5x - 4
= 16x + 5
a. For the smaller triangle:
Perimeter = (x + 3) + (2x - 5) + (x + 7)
= x + 3 + 2x - 5 + x + 7
= 4x + 5
b. To find the difference between the perimeter of the larger and smaller triangle, we subtract the perimeter of the smaller triangle from the perimeter of the larger triangle.
Difference = (16x + 5) - (4x + 5)
= 16x - 4x
= 12x
c. To find the perimeter of each triangle when x = 3, we substitute x = 3 into the expressions for the perimeters.
For the larger triangle:
Perimeter = 16x + 5
= 16(3) + 5
= 48 + 5
= 53
For the smaller triangle:
Perimeter = 4x + 5
= 4(3) + 5
= 12 + 5
= 17
Therefore, when x = 3, the perimeter of the larger triangle is 53 units, and the perimeter of the smaller triangle is 17 units.