The base of the triangle is 17. The other two sides are integers and one of the sides is twice as long as the other. What is the longest possible length of the side of the triangle.
shorter of the other sides --- x
longer of the other sides ---- 2x
To be a triangle the sum of any two sides must be greater than the third side
x+2x > 17 AND x+17>2x AND 2x+17>x
3x > 17 AND x < 17 AND x > -17
x > 17/3 AND x < 17
(x is between 5.666.. and 17)
the largest value of x we could have is 16
so the largest side can be 32
triangle is 16 by 17 by 32
check:
is 16+17>32 ? yes
is 16+32>17 ? yes
is 32+17>16 ? yes
To find the longest possible length of the side of the triangle, we can start by considering the relationship between the sides.
Let's assume that one of the sides is x. Since the other side is twice as long as x, the length of the other side can be written as 2x.
Using 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 the following inequalities:
x + 2x > 17 (as the sum of any two sides must be greater than the length of the third side)
3x > 17
x > 17/3
Since x must be an integer, the minimum value it can take is 6 (since 17/3 = 5.67).
So, the longest possible length of the side of the triangle is 2x. Therefore, the longest possible length is 2 * 6 = 12.
Hence, the longest possible length of the side of the triangle is 12.
To find the longest possible length of a side of the triangle, we need to consider the given information.
We know that the base of the triangle is 17 units. Let's call one of the other sides "x" and the remaining side "2x," as one side is twice as long as the other.
To determine the longest possible length of a triangle side, we can use the triangle inequality theorem. According to this theorem, for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.
Using this information, we can write the following inequality:
x + 2x > 17
Simplifying the equation, we get:
3x > 17
To find the largest possible value for x, we divide both sides of the inequality by 3:
x > 17/3
Since x must be an integer, the next largest integer value above 17/3 is 6. Therefore, the longest possible length of a side of the triangle is 2x = 2 * 6 = 12 units.
Hence, the longest possible length of the side of the triangle is 12 units.