Towns P, Q and R are connected by roads PQ ,PR and QR. PR is 10km longer than PQ QR is twice as long as PR.
The total length of three roads is 170km.
Work out length of PQ.​

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

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x