Question

The points O, P, Q and R all lie on the same line segment, in that order, such that the ratio of OP : PQ : QR is equal to 1 : 1 : 3. If OR = 10, find OQ.

Answer 1

OQ = 4

Explanation:

the ratios of the segments OP : PQ : QR = 1 : 1 : 3 = x : x : 3x ( x is a multiplier)

then

OP + PQ + QR = OR , that is

x + x + 3x = 10

5x = 10 ( divide both sides by 5 )

x = 2

Then

OQ = OP + PQ

= x + x

= 2x

= 2 × 2

= 4