a triangle has sides of length 7 cm ,15cm and x cm. If x is an interger find (i) the minimum value of x (ii) the maximum value of x
So for a triangle, two sides have to be greater than the largest side. Therefore, if you have three sides 7, 15, and x, you could say that...
a) x is the largest
b) 15 is the largest.
a) If x is the largest side then 7+15 has to be greater than x. 22 has to be greater than x. So x<22. There's the maximum value.
b) If 15 is the largest side, then x+7 has to be greater than 15. So x>8. That is the minimum value.
minimum=9
maximum=21
To find the minimum and maximum values of x in the triangle with sides of lengths 7 cm, 15 cm, and x cm, we can use the Triangle Inequality Theorem.
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.
(i) Minimum value of x:
To find the minimum value of x, we need to consider the smallest possible sum of the two given sides, which is 7 cm + 15 cm = 22 cm. Therefore, the minimum value of x would be the length of the remaining side, which is 22 cm - 15 cm = 7 cm.
(ii) Maximum value of x:
To find the maximum value of x, we need to consider the largest possible sum of the two given sides, which is 7 cm + 15 cm = 22 cm. Therefore, the maximum value of x would be the length of the remaining side, which is 22 cm - 7 cm = 15 cm.
So, the minimum value of x is 7 cm, and the maximum value of x is 15 cm.
To find the minimum value of x, we need to determine the smallest possible value for the missing side of the triangle. 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.
In this case, we have two known sides: 7 cm and 15 cm. Let's check the conditions using these sides and x as the third side:
Condition 1: 7 cm + 15 cm > x cm
Condition 2: 7 cm + x cm > 15 cm
Condition 3: 15 cm + x cm > 7 cm
(i) Minimum value of x:
We can start with Condition 1:
7 cm + 15 cm > x cm
22 cm > x cm
Therefore, the minimum value of x is 23 cm, as x must be larger than 22 cm in order to satisfy this inequality.
(ii) Maximum value of x:
For the maximum value of x, we consider Condition 3:
15 cm + x cm > 7 cm
x cm > -8 cm
Since x must be an integer, the maximum value is 0 cm, as any negative value would not be a valid side length for a triangle.
So, the minimum value of x is 23 cm, and the maximum value of x is 0 cm.