Question

4. Find the dimensions of the largest isosceles triangle having a perimeter of 18 cm. Answer ( all
sides 6 cm)

i really need help with coming up with the equation of the function before solving its derivative and making it equal zero

so far i know 2x+y=18

Answer 1

For an isosceles triangles with equal legs x, and base y, the height is
√(x²-(y/2)²), where the base length is given by
y=18-2x .....(1)

The area if such a triangle is:
A(x)
=(1/2)base*height
=(y/2)*√(x²-(y/2)²)...(2)

Substitute the value of y from equation (1) to reduce equation (2) to a function of x only.

Differentiate A(x) with respect to x and equate A'(x) to zero to determine the value of x to maximize the area.

Check that A"(x) is negative, i.e. A is a maximum.

I get x=6 (equilateral triangle).