The values of x and the side length are as follows:
a. x = 6 ; RS = 15; ST = 19; RT = 34;
b. x = 5 ; RS = 20; ST = 1; RT = 21;
How to write equation in terms of x?
Point S is between R and T.
Therefore, the equation in terms of x can be represented as follows:
RT = RS + ST
a.
RS = 4x - 9
ST = 19
RT = 8x - 14
Hence,
8x - 14 = 4x - 9 + 19
8x - 14 = 4x - 9 + 19
8x - 14 = 4x + 10
8x - 4x = 10 + 14
4x = 24
x = 24 / 4
x = 6
RS = 4x - 9 = 4(6) - 9 = 24 - 9 = 15
ST = 19
RT = 8x - 14 = 8(6) - 14 = 48 - 14 = 34
b.
RS = 2x + 10
ST = x - 4
RT = 21
Therefore,
21 = 2x + 10 + x - 4
21 = 3x + 6
21 - 6 = 3x
15 = 3x
divide both sides by 3
x = 15 / 3
x = 5
RS = 2x + 10 = 2(5) + 10 = 10 + 10 = 20
ST = x - 4 = 5 - 4 = 1
RT = 21
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