Answer:
33
Step-by-step explanation:
Step 1: The Diagonals of the Convex Quadilateral are Mutually Perpendicular this makes the shape a Rhombus Shape
Step 2: The formula for a area of a rhombus is the multiply the two lengths and divide by two.
In this Question we have x×y÷2 or xy/2
Step 3: The sum of the lengths of the diagonals is 12
x+y=12
y=12-x
Therefore, the area, as a function of x alone = x(12-x)/2
Step 4: To find the maximum area, let's find the derivative of the area function in respect to x and then equate to 0.
d/dx(x(12-x)/2)=0
d/dx(12x - x^2) = 0
12-2x=0
12-0=2x
12=2x, divide both sides by 2
x= 6
Step 5: Calculate the Maximum Area
The maximum area will then be 6(12 - 6)/2
= (72-6)/2 = 66/2= 33
So, the maximum area is 33.
