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We have, `|P|+|Q|=18N,|R|=|P+Q|+12N` <br> `alpha=90^(@)` <br> `P+Q cos theta=0` <br> `impliesQ cos theta=-P` <br> Now. `R^(2)=P^(2)+Q^(2)+2PQcostheta` <br> `impliesR^(2)+P^(2)+Q^(2)+2P(-P)=Q^(2)-P^(2)` <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/ARH_AAG_V_3DG_C01_SLV_031_S01.png" width="80%"> <br> `implies12^(2)=(P+Q)(Q-P)=18(Q-P)` <br> `impliesQ-P=8 and Q+P=18` <br> `impliesQ=13,P=5` <br> `therefore` magnitude of two forces are 5 N and 13N.