SOLUTION: a lot is in the shape of a right triangle. The hypotenuse is 3m longer than the longer leg. The longer leg is 6m longer than twice the length of the shorter leg. Find the perimeter

Question 233809: a lot is in the shape of a right triangle. The hypotenuse is 3m longer than the longer leg. The longer leg is 6m longer than twice the length of the shorter leg. Find the perimeter.
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
C=B+3 OR B=C-3
B=2A+6
C-3=2A+6
C=2A+9
A^2+B^2=C^2
A^2+(2A+6)^2=(2A+9)^2
A^2+4A^2+24A+36=4A^2+36A+81 CANCEL OUT THE 4X^2 TERMS & COMBINE LIKE TERMS:
A^2+24A-36A+36-81=0
A^2-12A-45=0 FACTOR THE EUATION.
(A-15)(A+3)=0
A-15=0
A=15 ANS. FOR THE SHORT LEG.
B=2*15+6=30+6=36 ANS. FOR THE LONG LEG.
C=36+3=39
FOR THE HYPOTENUSE.
PROOF:
15^2+36^2=39^2
225+1296=1521
1521=1521
THEREFORE THE PERIMETER=15+36+39=90 m.

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