Question

In front of a 200 meters long wall, a triangular plot is to be cordoned off using the wall as one of its sides and a fencing of total length 300 meters to form the other two sides. Then the maximum possible area (in square meters) of the plot that can be cordoned off is​

Answer 1

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• For maximum area of a rt angled triangle with a fixed hypotenuse, base and height should be equal.

• base = height = s

then 

• s^2+s^2= 100^2
• s^2= 0.5 *(100)^2

=> area of triangle = 1/2 *s*s = (1/4)*(100)^2= 50^2 = 2500 sq mtrs

Answer 2

Step-by-step explanation:

Point to remember : Maximum area is when we have a right angled triangle and the base and height are both equal.

Side 1 = 300 ( Given )

Side 2 = Side 3 ( Base = Height)

As we know 2 Other sides have a total length of 300

So, Side 1 = Side 2 = 150 each

Semi Perimeter = 250

s= ( 200+300)/2

Using Heron's formula,

$\sqrt{250(250 - 200)(250 - 150)(250 - 150)}$

Answer: 5000

$\sqrt{5}$