Question

Look at the given triangles.

4x+2, 7x+7, 5x-4

x+3, 2x-5, x+7

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

Answer 1

a. For the first triangle:
Perimeter = (4x+2) + (7x+7) + (5x-4)
Perimeter = 16x + 5

For the second triangle:
Perimeter = (x+3) + (2x-5) + (x+7)
Perimeter = 4x + 5

b. Difference in perimeter = Perimeter of larger triangle - Perimeter of smaller triangle
= (16x + 5) - (4x + 5)
= 12x

c. When x = 3:

For the first triangle:
Perimeter = (4(3)+2) + (7(3)+7) + (5(3)-4)
Perimeter = 32

For the second triangle:
Perimeter = (3+3) + (2(3)-5) + (3+7)
Perimeter = 12 + 1 + 10
Perimeter = 23