Question

∠PON≅∠PRQ. P, Q, equals, 12, point, 5PQ=12.5, P, R, equals, 17, point, 5PR=17.5, and Q, N, equals, 7, point, 5QN=7.5. Find the length of start overline, R, O, end overline
RO
. Round your answer to the nearest tenth if necessary.

RO = what

Answer 1

Interpret triangles ΔOPN and ΔRPQ as similar (∠PON ≅ ∠PRQ and the rays OP and RP coincide), so corresponding sides give

PN/PQ = OP/PR.

PN = PQ + QN = 12.5 + 7.5 = 20, so
OP = PR * (PN/PQ) = 17.5 * (20/12.5) = 17.5 * 1.6 = 28.

If O, P, R are collinear with P between them, RO = OP − PR = 28 − 17.5 = 10.5.

RO = 10.5.