Answer: RS = 16
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Explanation:
The ratio QR : RS : ST is equal to 1 : 4 : 5
This means we have the following three equations
For some positive number x.
Note the ratio QR : RS : ST turns into x : 4x : 5x, which reduces to 1 : 4 : 5 when we divide all three parts by x
.
Along with those three equations, we'll also use QT = 40 as well.
Now turn to the segment addition postulate. Plug in the equations mentioned earlier, and solve for x
.
QT = QR + RS + ST
40 = x+4x+5x
40 = 10x
10x = 40
x = 40/10
x = 4
So we know that
QR = x = 4
RS = 4x = 4*4 = 16
ST = 5x = 5*4 = 20
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As a check,
QR + RS + ST = 4 + 16 + 20 = 40
which is the same as QT = 40
Therefore, we've confirmed that QR + RS + ST = QT is correct and we've confirmed our answers.
