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
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
a. To find the perimeter of a triangle, we add the lengths of all three sides.
For the first triangle, the lengths are: 4x + 2, 7x + 7, 5x - 4.
The perimeter is: (4x + 2) + (7x + 7) + (5x - 4) = 16x + 5.
For the second triangle, the lengths are: x + 3, 2x - 5, x + 7.
The perimeter is: (x + 3) + (2x - 5) + (x + 7) = 4x + 5.
b. To find the difference in perimeter between the two triangles, we subtract the perimeter of the smaller triangle from the perimeter of the larger triangle.
The difference is: (16x + 5) - (4x + 5) = 12x.
c. To find the perimeters when x = 3, we substitute x = 3 into the expressions we found in part a.
For the first triangle, the perimeter is: 16(3) + 5 = 53.
For the second triangle, the perimeter is: 4(3) + 5 = 17.
Therefore, the perimeter of the first triangle when x = 3 is 53 units, and the perimeter of the second triangle when x = 3 is 17 units.