Question
If the sum of the lengths of hypotenuse and a side of a right angled triangle is given, show that the area is maximum when the angle between them is 60°.
Solution
Let ABC be a triangle in which AB = x, AC – y, ∠BAC = 6
.
From given conditon,
...(1)
where k is constant.
Let ∆ be area of ∆ABC.
Let ∆ be area of ∆ABC.
Now,
gives us
.From given conditon,
...(1)where k is constant.
Let ∆ be area of ∆ABC.
Let ∆ be area of ∆ABC.
Now,
gives us 
