Question

CHALLENGE. Point K is between points J and L . If J K=x²-4 x, K L=3 x-2 , and J L=28 , write and solve an equation to find the lengths of J K and K L .

Answer 1

Explanation:

We can use the fact that the sum of the lengths of J and is equal to the length of JK + KL = JL.

So, we have:

JK + KL = JL

Substituting the given values, we get:

(x^2 - 4x) + (3x - 2) = 28

Simplifying and solving for x, we get:

4x^2 - 8x - 26 = 0

Dividing by 2, we get:

2x^2 - 4x - 13 = 0

Using the quadratic formula, we get:

x = [4 ± sqrt(16 + 104)] / 4

x = [4 ± sqrt(120)] / 4

x = [4 ± 2sqrt(30)] / 4

x = 1 ± 0.5sqrt(30)

Note that we reject the negative solution for x, since length cannot be negative.

Therefore, the length of JK is:

JK = x^2 - 4x = (1 + 0.5sqrt(30))^2 - 4(1 + 0.5sqrt(30)) ≈ 5.185

And, the length of KL is:

KL = 3x - 2 = 3(1 + 0.5sqrt(30)) - 2 ≈ 3.46

Therefore, the lengths of JK and KL are approximately 5.185 and 3.46, respectively.