Question

In triangle ABC, where side BC = 8 cm and AC = x + 2 cm, and the perimeter is 30 cm, form an equation and solve for the length of side AC.

Answer 1

To find the length of side AC, we use the perimeter formula: P = a + b + c, substituting known values to get a formula in terms of x, then solve for x to find AC as x + 2 cm.

Step-by-step explanation:

To solve for the length of side AC in triangle ABC with side BC = 8 cm and side AC = x + 2 cm, while knowing the perimeter is 30 cm, we can use the perimeter formula for a triangle. First, we let AB be represented by side a, BC by side b (which is 8 cm), and AC by side c (which is x + 2 cm). We can then express the perimeter P of the triangle as:

P = a + b + c

Substituting known values, we get:

30 cm = a + 8 cm + (x + 2 cm)

Simplifying the equation:

30 cm = a + x + 10 cm

From this, we can solve for 'a':

a = 20 cm - x

Given that a, b, and c are the sides of the triangle, 'a' must be some positive value, so x must be less than 20 cm to maintain a physical triangle. We thus have a system of equations to work with:

1. 
   
2. a = 20 cm - x
3. 
   
4. b = 8 cm
5. 
   
6. c = x + 2 cm (this is the side we need to find)

Once 'a' is determined, the length of AC can be found by adding 2 cm to the value of x.