Question 683731: if a and b are lenghts of the leg of a right angel triangle whose hypothenos is 10 and area is 20 what is the value of a pluse b all squered
Answer by Jolliano(16)   (Show Source):
You can put this solution on YOUR website! Let the sides of the triangle be a and b and the hypotenus be c.
From Pythagoras theorem,
a^2 + b^2 = c^2
=10^2 =100
Therefore,
a^2 + b^2 = 100.....(1)
Also,
area of the triangle =(1/2)absinc
20 =(1/2)absin90
20 =(1/2)ab * 1
Multiply through by 2
40 = ab.....(2)
Now,
(a+b)^2 = (a+b)(a+b)
=a^2 + 2ab + b^2
=(a^2 +b^2) +2(ab).
Now substitue the values in equations 1 and 2.
(a^2 +b^2) +2(ab) =
(100) + 2(40) =
100 + 80 =180
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