PQR is a right triangle in which the hypotenuse PR is 8m more than the side PQ. If QR is 7m more than PQ, find the dimensions of the triangle PQR.

Dear student
Let the length of PQ be x.Then Hypotenuse=x+8and QR=x+7By pythagoras Theorem,H2=P2+B2x+82=x2+x+72x2+64+16x=x2+x2+49+14x15+2x=x2x2-2x-15=0x=--2±-22-4-152x=2±4+602x=2±642x=2±82x=5 or x=-3(which is not possible)So x=5mHence,PQ=5mHypotenuse=5+8=13mQR=5+7=12m

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