<PRE><B>Question 500319</B>
Area f triangle = 150 = 1/2ab
ab = 300
a^2 + b^2 = c^2.
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a + b + c = 60; the perimeter.
a+ b = 60 - c rearrangement.
square both sides.
(a + b)^2 = (60 - c)^2
a^2 + 2ab + b^2 = 3600 + c^2 - 120c
subtract the equation A^2 + b^2 = c^2 (simultaneous equations)
2ab = 3600 - 120c
ab is known to be 300, hence
600 = 3600 - 120c
-3000 = -120c
25 = c
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substitute c by 25 in the equation a + b + c = 60  to obtain
a + b + 25 = 60
a + b = 35
Since AB = 300 then b = 300/a which is substituted into the equation a + b = 35
a + 300/a  - 35 = 0
multiply all terms by a.
a^2  -35a + 300 = 0
Solve our quadratic equation.
(x -15)(x - 20)
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15, 20, 25 are our dimensions.
15 + 20 + 25 = 60 units perimeter.
This does check.
15 * 20 = 300 units area.
This does check.
15^2 + 20^2 = 25^2 
225 + 400 = 625 units.
This does check also.
Cleomenius
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