One side of a triangle is 4 cm longer than the shortest side and 2 cm shorter than the longest side. The perimeter is 38 cm. Find the dimensions of the triangle.
x+x-2+x+4=38
3x+2=38
3x=36
x=12
12, 10, 16
PT=sum of all sides
38=x+(x-2)+(x+4)
38=x+x-2+x+4
38=x+x+x-2+4
38=3x+2
38-2=3x
36=3x
36/3=3x/3
12=x
one side is 12
12-2=10
the other side is 10
12+4=16
the last side is 16
Let's denote the shortest side of the triangle as x cm.
According to the given information, one side of the triangle is 4 cm longer than the shortest side, so the second side would be (x + 4) cm.
Similarly, one side is 2 cm shorter than the longest side, so the third side would be (x + 4 + 2) cm, which can be simplified to (x + 6) cm.
The perimeter of a triangle is the sum of all its sides. According to the question, the perimeter is 38 cm. So we can write the equation:
x + (x + 4) + (x + 6) = 38
Simplifying the equation:
3x + 10 = 38
Subtracting 10 from both sides:
3x = 38 - 10
3x = 28
Dividing both sides by 3:
x = 28 / 3
x ≈ 9.33 cm
So, the shortest side of the triangle is approximately 9.33 cm.
Now, we can substitute this value back into the expressions for the other sides:
Second side: x + 4 ≈ 9.33 + 4 ≈ 13.33 cm
Third side: x + 6 ≈ 9.33 + 6 ≈ 15.33 cm
Therefore, the dimensions of the triangle are approximately:
Shortest side: 9.33 cm
Second side: 13.33 cm
Third side: 15.33 cm
To solve this problem, let's assign variables to the sides of the triangle. Let's call the shortest side "x" cm. Since one side is 4 cm longer than the shortest side, the second side can be expressed as "x + 4" cm. Similarly, as one side is 2 cm shorter than the longest side, we can represent the longest side as "x + 6" cm.
According to the given information, the perimeter of the triangle is 38 cm. The perimeter of a triangle is the sum of the lengths of its sides. Therefore, we can write the equation:
x + (x + 4) + (x + 6) = 38
Simplifying this equation, we get:
3x + 10 = 38
Subtracting 10 from both sides of the equation:
3x = 28
Finally, dividing both sides of the equation by 3:
x = 28 / 3
Therefore, the shortest side of the triangle is approximately 9.33 cm.
Substituting this value back into our expressions for the other sides:
Shortest side = x = 9.33 cm
Second side = x + 4 = 9.33 + 4 = 13.33 cm
Longest side = x + 6 = 9.33 + 6 = 15.33 cm
Thus, the dimensions of the triangle are approximately: 9.33 cm, 13.33 cm, and 15.33 cm.