given triangle QRS=triangle TUV, QR=2x=7, RS=13,and QS=3x+2 and TV=7x-6 find the value of x

if they are equal, then QR=TU; RS=UV; and QS=TV. Using this last equality, one gets...

3x+2=7x-6
solve for x.

To find the value of x, we need to set up an equation equating corresponding sides of the two triangles QRS and TUV.

Given that QR = 2x + 7, RS = 13, QS = 3x + 2, and TV = 7x - 6, we can equate the corresponding sides:

QR = TV (corresponding sides of triangle QRS and TUV)

Substituting the given values:

2x + 7 = 7x - 6

Now, let's solve for x:

2x - 7x = -6 - 7

-5x = -13

Dividing both sides of the equation by -5:

x = (-13) / (-5)

x = 13 / 5

Therefore, the value of x is 13/5 or 2.6.