Note: For questions 22–23, your teacher will grade your response to ensure you receive proper credit for your
answer.
22. Look at the given triangles.
a. Write an expression in simplest form for the perimeter of each triangle.
b. Write another expression in simplest form that shows the difference between the perimeter
of the larger triangle and the perimeter of the smaller triangle.
c. Find the perimeter for each triangle when x = 3
16x+5-4x+5
The given expression is 16x + 5 - 4x + 5.
Combining like terms, we can add the constants 5 and 5 to get:
= 16x + 10 - 4x
Now, we can combine the x-terms by subtracting 4x from 16x to get:
= 12x + 10
Therefore, the simplified expression is 12x + 10.
To find the perimeter of a triangle, you need to add up the lengths of all the sides.
a. Let's look at the given triangles:
Triangle 1:
Side A = 4x + 7
Side B = 3x + 5
Side C = 2x + 3
The perimeter of Triangle 1 would be:
Perimeter = Side A + Side B + Side C = (4x + 7) + (3x + 5) + (2x + 3)
Triangle 2:
Side A = 5x + 2
Side B = 2x + 6
Side C = 3x + 1
The perimeter of Triangle 2 would be:
Perimeter = Side A + Side B + Side C = (5x + 2) + (2x + 6) + (3x + 1)
b. To find the difference between the perimeter of the larger triangle and the perimeter of the smaller triangle, you subtract the two perimeters. Let's say Triangle 1 is the smaller triangle and Triangle 2 is the larger triangle.
Difference = Perimeter of Triangle 2 - Perimeter of Triangle 1
Difference = [(5x + 2) + (2x + 6) + (3x + 1)] - [(4x + 7) + (3x + 5) + (2x + 3)]
c. To find the perimeter for each triangle when x = 3, substitute x = 3 into the expressions we derived in parts a and b.
Perimeter of Triangle 1 with x = 3:
Perimeter = (4(3) + 7) + (3(3) + 5) + (2(3) + 3)
Perimeter of Triangle 2 with x = 3:
Perimeter = (5(3) + 2) + (2(3) + 6) + (3(3) + 1)
a. Triangle 1: 2x + 7 + x = 3x + 7
Triangle 2: 4x + 4 + 2x = 6x + 4
b. (6x + 4) - (3x + 7) = 3x - 3
c. Triangle 1: 2(3) + 7 + 3 = 13
Triangle 2: 4(3) + 4 + 2(3) = 22