12. A triangle has side lengths as follows: 2x - 3, 8x + 1 and 5x - 8. Find an expression to find the perimeter of the triangle and solve for x, to find each side length. If the Perimeter is equal to 215 inches.

Step-by-step explanation:

The perimeter of a plane figure is the distance around it. The formula for determining the perimeter of a triangle is expressed as

Perimeter = a + b + c

Where a, b and c are the length of each side of the triangle.

The triangle has side lengths as follows: 2x - 3, 8x + 1 and 5x - 8. Therefore, the expression to find the perimeter of the triangle is

2x - 3 + 8x + 1 + 5x - 8

= 2x + 8x + 5x - 3 + 1 - 8

= 15x - 10

If the Perimeter is equal to 215 inches, it means that

15x - 10 = 215

15x = 215 + 10 = 225

x = 225/15

x = 15

The length of the sides are

2x - 3 = 2 * 15 - 3 = 27 inches

8x + 1 = 8 * 15 + 1 = 121 inches

5x - 8 = 5 * 15 - 8 = 67 inches

15x - 10 = P

Step-by-step explanation:

(2x - 3) + (8x + 1) + (5x - 8) = 215

2x - 3 + 8x + 1 + 5x - 8 = 215

collect the like terms

15x - 10 = 215

add 10 to each side

15x = 225

divide each side by 15

x = 15

sub x = 15 into the original equation

2 (15) - 3 + 8 (15) + 1 + 5 (15) - 8 = 215

therefore the expression to find the perimeter (P) o the triangle is:

15x - 10 = P