Question

Look at the given triangles.
4x+1 5x+5 7x-2

2x+2 6x+2 X+6

A)Write an expression 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 smaller triangle.

C)Find the perimeter for each triangle when x = 2.

Answer 1

A) The perimeter of a triangle is the sum of the lengths of its three sides. Therefore, the perimeter of the first triangle is:

4x+1 + 5x+5 + 7x-2 = 16x + 4

And the perimeter of the second triangle is:

2x+2 + 6x+2 + x+6 = 9x + 10

B) To find the difference between the perimeters, we subtract the smaller from the larger:

(9x + 10) - (16x + 4) = -7x + 6

C) To find the perimeter of each triangle when x = 2, we simply substitute 2 for x in the expressions we found in part A:

Perimeter of first triangle: 16(2) + 4 = 36

Perimeter of second triangle: 9(2) + 10 = 28