In triangle ABC,

BC=2x

Ac=x+10

permiter=42=x+2x + 10+x
solve for x

19

To solve this problem, we need to set up an equation and solve for the value of x. Then, we can substitute the value of x into the given information to find the lengths of the sides of the triangle.

Let's start by setting up the equation using the given information:

AB + BC + AC = Perimeter

Since AB is x cm long, and BC is twice the length of AB, we can write BC as 2x. Similarly, AC is 10 cm longer than AB, so we can write AC as (x + 10).

Substituting these values into the equation, we get:

x + 2x + (x + 10) = 42

Now we can solve for x:

4x + 10 = 42
4x = 42 - 10
4x = 32
x = 32 / 4
x = 8

Now that we have found the value of x, we can substitute it back into the given information to find the lengths of the sides of the triangle:

AB = 8 cm
BC = 2x = 2(8) = 16 cm
AC = x + 10 = 8 + 10 = 18 cm

Therefore, the lengths of the sides of the triangle are:
AB = 8 cm
BC = 16 cm
AC = 18 cm