Question

1. in the figure to the right, pr = 13 inches and qr = 4 inches. find pq.
2. in the figure to the right, qr = 45 feet and rs = 15 feet. find qs.
3. in the figure to the right, eg = 12, ef = 2x - 3 and fg = x + 6. find ef and fg.

Explanation:

Step1: Use segment - addition postulate

For the first problem, if $PR = 13$ inches and $QR = 4$ inches, and $PR=PQ + QR$, then $PQ=PR - QR$.
$PQ=13 - 4$

Step2: Calculate the value of $PQ$

$PQ = 9$ inches

For the second problem, if $QR = 45$ feet and $RS = 15$ feet, and $QS=QR + RS$
$QS=45+15$
$QS = 60$ feet

For the third problem, since $EG = EF+FG$ and $EG = 12$, $EF = 2x - 3$, $FG=x + 6$
We have the equation $(2x - 3)+(x + 6)=12$

Step1: Combine like - terms

$2x-3+x + 6=12$
$3x+3 = 12$

Step2: Solve for $x$

Subtract 3 from both sides: $3x=12 - 3$
$3x=9$
Divide both sides by 3: $x = 3$

Step3: Find $EF$ and $FG$

$EF=2x - 3=2\times3-3=3$
$FG=x + 6=3 + 6=9$

Answer:

1. $PQ = 9$ inches
2. $QS = 60$ feet
3. $EF = 3$, $FG = 9$