solve for x if△LMN≅△QRS, LM=2x+11 and QR=3x-9
since △s are congruent, LM≅QR, so
2x+11 = 3x-9
x = 20
To solve for x in the given problem, we will use the fact that congruent triangles have corresponding sides that are equal in length.
According to the given information, △LMN≅△QRS, which means that their corresponding sides are equal in length. Specifically, LM is congruent to QR.
Given:
LM = 2x + 11
QR = 3x - 9
We can set up the equation to equate the lengths of LM and QR:
2x + 11 = 3x - 9
To solve for x, we need to isolate the variable. Let's move the terms involving 'x' to one side and the constant terms to the other side:
2x - 3x = -9 - 11
Simplifying:
-x = -20
To get rid of the negative sign in front of 'x', we'll multiply both sides of the equation by -1:
(-1)(-x) = (-1)(-20)
This simplifies to:
x = 20
Therefore, the value of x is 20.
To solve for x, we need to use the fact that the two triangles, △LMN and △QRS, are congruent. This means that their corresponding sides must be equal in length. In this case, we know that LM is equal to QR. So we can set up an equation and solve for x.
Given:
LM = 2x + 11
QR = 3x - 9
Setting the two sides equal to each other:
2x + 11 = 3x - 9
Now, let's solve for x.
First, we want to isolate the x terms on one side of the equation. To do this, we can subtract 2x from both sides of the equation:
2x + 11 - 2x = 3x - 9 - 2x
Simplifying the equation:
11 = x - 9
Next, let's isolate the x term on one side. We can add 9 to both sides of the equation:
11 + 9 = x - 9 + 9
Simplifying the equation further:
20 = x
Therefore, x = 20.
To confirm our answer, we can substitute x = 20 into the original equations:
LM = 2(20) + 11 = 51
QR = 3(20) - 9 = 51
The lengths of LM and QR are indeed equal, so x = 20 is the correct solution.