SOLUTION: If the perimeter of a right angle triangle equals 30cm, and its area is 30cm squared. Find the length of the sides.

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Question 678160: If the perimeter of a right angle triangle equals 30cm, and its area is 30cm squared.
Find the length of the sides.
Answer by sachi(548) About Me  (Show Source):
You can put this solution on YOUR website!
let AB & AC are two legs of the triangle angle A=90 deg & BC is hypotenuse
so AB^2+AC^2=BC^2...........1
the perimeter of a right angle triangle equals 30 cm
so AB+BC+CA=30..............2
its area is 30cm squared.
so 1/2*AB*AC=30
or AB*AC=60................3
from 2
AB+AC=30-BC
squaring both sides
AB^2+AC^2+2AB*AC=900+BC^2-2*30*BC
substituting the values from 1&3
BC^2+2*60=900+BC^2-60BC
or 60BC=900-120=780
or BC=13 ans
now above eqns 1&2modified to
AB^2+AC^2=13^2=169..........4
now (AB-AC)^2=AB^2+AC^2-2AB*AC=169-2*60=49
or AB-AC=+/-7......5
from eqn 2
AB+13+AC=30
or AB+AC=30-13=17.....6
adding eqns 5&6
2AB=24 or 10
so AB= 12 or 5 ans
putting these values in eqn 6
AC=5 or 12 ans
so AB=12 BC-13 & AC=5 one set solns
& AB=5 BC-13 & AC=12 the other set solns
sorry for the mistake in earlier soln
thnx