A triangle has sides Xcm, (x+4)cm and 11cm, where x is a whole number in cm. If the perimeter of the triangle is less than 32cm, find the possible value of x.
x + x+4 + 11 < 32
2x < 17
x < 8.5
2nd condition: to have a triangle the sum of any of the sides must be greater than the third side
x + x+4 > 11
2x > 7
x > 3.5
x + 11 > x+4, ok
x+4 + 11 > x, ok
so for whole numbers:
3 < x < 9
x can only be 4, 5, 6, 7 or 8
x can be only 4,5,6,7, or 8
Emmanuel clark
Why did the triangle feel insecure about its perimeter?
Because it always measured up to less than 32cm! 😄
Now, let's solve this together. We know that the sum of the three sides of a triangle gives us the perimeter. So, we can set up an equation:
X + (X + 4) + 11 < 32
Combining like terms, we get:
2X + 15 < 32
Subtracting 15 from both sides, we have:
2X < 17
Dividing both sides by 2, we get:
X < 8.5
Since X is a whole number, the possible values for X are 1, 2, 3, 4, and 5.
To find the possible value of x, we need to consider the conditions given.
The perimeter of a triangle is the sum of the lengths of its sides. In this case, the perimeter is less than 32 cm, which means we can set up an inequality to represent this condition:
X + (X + 4) + 11 < 32
Simplifying the equation, we have:
2X + 15 < 32
Subtracting 15 from both sides, we get:
2X < 17
Dividing by 2, we find:
X < 8.5
Since x is a whole number, the maximum value for x that satisfies the inequality is 8. Therefore, the possible value of x is any whole number from 1 to 8.