Grade 10Algebra
In an acute angled triangle PQR,angle PQR=45 degree.Prove that (PR)2=(PQ)2+(QR)2-4ar(trianglePQR).
In an acute angled triangle PQR,angle PQR=45 degree.Prove that (PR)2=(PQ)2+(QR)2-4ar(trianglePQR).
1 Answer
ATHARV DEO
construct PN perpendicular to QR
in triangle PNQ, angle Q=45
so QN=PN
PQ^2+QR^2-4*areaPQR=PN^2+QN^2+(QN+NR)2-4*0.5*QR*PN
=2PN^2+PN^2+NR^2+2*PN*NR-2*QR*PN
=2PN^2+PR^2+2PN.NR-2(PN+NR)*PN
=2PN^2-2PN^2+2PN*NR-2PN*NR+PR^2
Other Related Questions on algebra
How do you write “the product of 18 and q” as an algebraic expression?
How do you write “the product of 18 and q” as an algebraic expression?
algebra
Last Activity: 2 Years ago