Q. 345.0( 1 Vote )
Find the largest
• The triangle is right angled triangle.
• Hypotenuse is 5cm.
Let us consider,
• The base of the triangle is ‘a’.
• The adjacent side is ‘b’.
Now AC2 = AB2 + BC2
As AC = 5, AB = b and BC = a
25 = a2 + b2
b2 = 25 – a2 ---- (1)
Now, the area of the triangle is
Squaring on both sides
Substituting (1) in the area formula
For finding the maximum/ minimum of given function, we can find it by differentiating it with a and then equating it to zero. This is because if the function Z (x) has a maximum/minimum at a point c then Z’(c) = 0.
Differentiating the equation (2) with respect to a:
To find the critical point, we need to equate equation (3) to zero.
[as a cannot be zero]
Now to check if this critical point will determine the maximum area, we need to check with second differential which needs to be negative.
Consider differentiating the equation (3) with a:
Now let us find the value of
As , so the function A is maximum at
Substituting value of A in (1)
Now the maximum area is
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