Question

In triangle 4JKL, we have JK = 9 and KL = 15. If JL is an integer, what are the largest and smallest possible values for JL?

Answer 1

The largest possible value is 23

The smallest is 7

Explanation:

To get the length of JL, we use the triangle inequality theorem

The theorem is that the sum of the measure of any two sides of a triangle must be greater than the measure of the third side of the triangle for the triangle to exist

With respect to this, 9 + 15 must be greater than JL

since JL is an integer ( integers are whole numbers); we have the following

9 + 15 = 24

JL is less than 24; so the nearest integer closest to 24 is 23

Now, let us get the smallest possible value

For the smallest possible value;

Let us call that x

9 + x > 15

15 + x > 9

From the first inequality;

x > 15-9

x > 6

The smallest integer greater than is 7

So the smallest possible value for JL is 7 and the largest is 23