Angle JKL is congruent to angle MNP, KL= 21x - 2, NP = 20x, LJ = 15x, PM = 13x + 4. Find LJ.
I don't understand how to do it! Please, help! :)
To find the value of LJ, we need to set up an equation using the given information.
Since angle JKL is congruent to angle MNP, their corresponding sides are also congruent. This means that KL is equal to NP and LJ is equal to PM.
Given:
KL = 21x - 2
NP = 20x
Equating KL and NP:
21x - 2 = 20x
Next, we'll find the value of x:
21x - 20x = 2
x = 2
Now that we have the value of x, we can substitute it back into the given information to find LJ:
LJ = 15x
LJ = 15 * 2
LJ = 30
Therefore, LJ is equal to 30.
To solve this problem, we can start by setting up an equation based on the given information. We know that angle JKL is congruent to angle MNP, which means they have the same measure. Let's denote this measure as y.
So, we have:
JKL = MNP
Now, let's express the lengths KL, NP, LJ, and PM in terms of x:
KL = 21x - 2
NP = 20x
LJ = 15x
PM = 13x + 4
Since angle JKL is congruent to angle MNP, the corresponding sides KL and NP must be equal in length.
So, we can set up the equation:
KL = NP
Substituting the given expressions:
21x - 2 = 20x
Now, we can solve for x:
21x - 2 - 20x = 0
x - 2 = 0
x = 2
By substituting the value of x back into the expressions for KL, LJ, and PM, we can find the lengths:
KL = 21x - 2 = 21(2) - 2 = 42 - 2 = 40
LJ = 15x = 15(2) = 30
PM = 13x + 4 = 13(2) + 4 = 26 + 4 = 30
Therefore, LJ = 30.
Because the two triangles are congruent, the following pairs of side lengths are equal: JK = MN, KL = NP and LJ = PM
The last two relationships tell you that
21x - 2 = 20x, and 15x = 13x + 4
Both of those equations tell you that x = 2. (The gave you more information than you need to solve the problem!)
Since x = 2, LJ = 4