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Find the length of RT and ST.

Given:
[tex]\[ RT = 8x - 6 \][/tex]
[tex]\[ RS = 16 \][/tex]
[tex]\[ ST = 2x - 4 \][/tex]

Sagot :

GinnyAnsweridn
Let's solve the problem step-by-step. We are given the following:

- RT = 8x - 6
- RS = 16
- ST = 2x - 4

We know that RT is the sum of RS and ST:

RT = RS + ST

Substitute the given expressions into this equation:

8x - 6 = 16 + 2x - 4

Now, let's simplify and solve for [tex]\( x \)[/tex]:

8x - 6 = 12 + 2x

To isolate [tex]\( x \)[/tex], we first subtract [tex]\( 2x \)[/tex] from both sides:

8x - 2x - 6 = 12

6x - 6 = 12

Next, we add 6 to both sides to further isolate [tex]\( x \)[/tex]:

6x - 6 + 6 = 12 + 6

6x = 18

Now, we divide by 6:

x = 18 / 6

x = 3

Now that we have the value of [tex]\( x \)[/tex], we can substitute it back into the expressions for RT and ST to find their lengths.

RT = 8x - 6

RT = 8(3) - 6

RT = 24 - 6

RT = 18

Similarly, for ST:

ST = 2x - 4

ST = 2(3) - 4

ST = 6 - 4

ST = 2

So, the lengths are:

- RT = 18
- ST = 2

Thus, using these calculations, we have determined that the length of RT is 18 units and the length of ST is 2 units.
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