The perimeter of a triangle is 24 cm. One side is 2 cm longer than the shortest side. The longest side is 2 cm less than twice the length of the shortest side. Find the length of each side of the triangle.- write equation and solve.
Let x = shortest side
24 = x + (x + 2) + (2x - 2)
24 = 4x
24/4 = x
6 = x
Khud karo
Sum of all three sides is perimeter
Let length of shortest side be x
Other sides becomes (x+2) and (2x-2)
X+(x+2)+(2x-2)=24
4x=24
X=6
To solve this problem, let's first assign variables to represent the lengths of the sides of the triangle.
Let x be the length of the shortest side.
Since one side is 2 cm longer than the shortest side, the length of the second side is x + 2 cm.
And the longest side is 2 cm less than twice the length of the shortest side, so its length is 2x - 2 cm.
The perimeter of a triangle is the sum of the lengths of its three sides.
Therefore, we can write the equation for the perimeter of this triangle as:
x + (x + 2) + (2x - 2) = 24
Let's solve this equation to find the value of x:
Combining like terms:
4x = 24
Dividing both sides by 4:
x = 6
Now that we have found the value of x, we can substitute it back into the expressions for the other sides to find their lengths:
The length of the second side is x + 2 = 6 + 2 = 8 cm.
And the length of the longest side is 2x - 2 = 2(6) - 2 = 12 - 2 = 10 cm.
So, the lengths of the sides of the triangle are:
Shortest side: 6 cm
Second side: 8 cm
Longest side: 10 cm.