The sides of a triangle are x cm,x+3 cm and 10 cm.if x is a whole number of cm,find the lowest value of x. (Hint:The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
I need some one to solve it
Perimeter of triangle= x+(x+3)+10
Thus,x+(x+3)+10>x
2x+13>x
Not quite,
you did not read their hint and use their hint
the property you are looking at is this, and as they state:
the sum of any two sides of a triangle must be greater than the third side, so
x + x+3 > 10 and x + 10 > x+3 and x+3 + 10 > x
2x > 7 and 10> 3 (always true) and 13 > 0 (always true)
x > 7/2
so x > 7/2
Test it:
let x = 1 , the sides are 1,4, 10 . That cannot form a triangle
let x = 5, the sides are 5,8 and 10. That works
let x = 3.5001, the sides are 3.5001, 6.5001, and 10. Yup! Very skinny triangle.
To find the lowest value of x, we need to check the given condition for the triangle inequality.
According to the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So, we can write the following inequalities:
x + (x + 3) > 10
2x + 3 > 10
2x > 7
x > 3.5
Since x has to be a whole number of cm, the lowest possible value for x is 4 cm.
To solve this, we can start with x = 3 and check if it satisfies the inequalities.
For x = 3, the lengths of the sides would be 3 cm, 6 cm (3 + 3), and 10 cm. However, the sum of the two shorter sides (3 cm and 6 cm) is not greater than the length of the longest side (10 cm). Therefore, x = 3 is not a valid solution.
Next, we try x = 4. For x = 4, the lengths of the sides would be 4 cm, 7 cm (4 + 3), and 10 cm. Now, the sum of the two shorter sides (4 cm and 7 cm) is greater than the length of the longest side (10 cm). Hence, the lowest valid value for x is 4 cm.