The distance from P to Q is four times the distance from Q to R. The distance from p to r is 120 metres. What is the distance fr
2 answers:
Let distance from Q to R equal x. Then distance from P to Q is 4x. So we have something like this:
P-------------Q-----R
4x x
Distance all the way from P to R is 4x + x = 5x, and this must be equal to 120. So set up the equation:
Divide both sides by 5 to isolate x:
This is the length of QR.
Check to be sure:
P-------------Q-----R
4(24) + 24
96 + 24 = 120
Works!
P-------------Q-----R
4x x
Distance all the way from P to R is 4x + x = 5x, and this must be equal to 120. So set up the equation:
Divide both sides by 5 to isolate x:
This is the length of QR.
Check to be sure:
P-------------Q-----R
4(24) + 24
96 + 24 = 120
Works!
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If line AB and BC are intersecting at point B and ray BD bisect the angle ABC, then the value of x is 23
The line AB and BC are intersecting at point B.
Ray BD bisect the angle ABC
∠ABD = x+8 degrees
∠ABD=∠DBC = x+8
Because the ray BD bisect the ∠ABC, so ∠ABD and ∠DBC will be equal
∠ABD+∠DBC= 4x-30 degrees
Because both are vertically opposite angles
Substitute the values in the equation
x+8 + x+8 = 4x-30
2x+16 = 4x-30
2x-4x = -30-16
-2x = -46
x = 23
Hence, if line AB and BC are intersecting at point B and ray BD bisect the angle ABC, then the value of x is 23
The complete question is
Line AB and BC are intersecting at point B and ray BD bisect the angle ABC. What is the value of x?
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