In triangle ABC,
• AB is x cm long
• BC is twice the length of AB
• AC is 10 cm longer than AB.
The perimeter of the triangle is 42 cm.
Write down an equation in x and solve it.
Use your answer to find the lengths of the sides of the triangle.
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