Question

1. what is kl?

image of a right triangle jkl with right angle at j, jk = 9 cm, jl = 40 cm (note: likely typo, should be jl or j to l horizontal side is 40 cm, and jk is vertical 9 cm)

Explanation:

Step1: Identify the triangle type

The triangle \( \triangle KJL \) is a right - triangle with \( \angle J = 90^{\circ} \), \( KJ=9\space cm \) and \( JL = 40\space cm \). We can use the Pythagorean theorem \( c^{2}=a^{2}+b^{2} \) (where \( c \) is the hypotenuse and \( a,b \) are the legs of the right - triangle) to find the length of \( KL \).

Step2: Apply the Pythagorean theorem

For right - triangle \( \triangle KJL \), let \( a = KJ=9\space cm \), \( b = JL = 40\space cm \) and \( c=KL \). According to the Pythagorean theorem:
\[

$$\begin{align*} KL^{2}&=KJ^{2}+JL^{2}\\ KL^{2}&=9^{2}+40^{2}\\ KL^{2}&=81 + 1600\\ KL^{2}&=1681 \end{align*}$$

\]

Step3: Find the value of \( KL \)

Take the square root of both sides of the equation \( KL^{2}=1681 \). Since \( KL \) represents the length of a side of a triangle, it must be positive. So \( KL=\sqrt{1681}=41\space cm \).

Answer:

The length of \( KL \) is \( 41\space cm \).