Answer:
PQ = 35 km
Step-by-step explanation:
Here, we want to get the length of PQ
Let PQ = x
PR is 10 km longer than PQ
PR = 10 + x
QR = 2 * PR
QR = 2(10 + x)
Adding all gives 170;
x + 10 + x + 2(10 + x) = 170
2x + 10 + 20 + 2x = 170
4x + 30 = 170
4x = 170-30
4x = 140
x = 140/4
x = 35 km
PQ = 35 km
The length of the road PQ of the town where, towns P, Q and R are connected by roads PQ ,PR and QR is 35 km.
Length of line segment (say YX) is the distance of both the ends of it (y to x).
Towns P, Q and R are connected by roads PQ ,PR and QR.
The line segment PR is 10 km longer than PQ. Therefore,
[tex]PR=PQ+10\\PQ=PR-10[/tex] ......1
The line segment QR is twice as long as the line segment PR. Therefore,
[tex]QR=2PR[/tex] .....2
The total length of three roads is 170 km. Therefore,
[tex]PQ+PR+QR=170[/tex]
Put the value of PR and QR from equation 1 and 2 in the above equation as,
[tex](PR-10)+PR+(2PR)=170\\PR-10+PR+2PR=170\\4PR=170+10\\PR=\dfrac{180}{4}\\PR=45\rm km[/tex]
As the line segment PR is 10 km longer than PQ and length of PR is 45 km. Therefore,
[tex]PR=45-10\\PR=35\rm km[/tex]
Hence, the length of the road PQ of the town where, towns P, Q and R are connected by roads PQ ,PR and QR is 35 km.
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