Donald W. answered • 04/06/22
Experienced and Patient Tutor for Math and Computer Science
You could use Heron's formula for the area of a triangle using just the semi-perimeter and the length of the sides to figure this out. Recall that Heron's formula is :
A = √(s*(s-a)*(s-b)*(s-c))
Where s is the semi-perimeter and a, b, and c are the length of the sides. Since we know this is an isosceles triangle, we can label the three sides as x, x, and 18-2x. So the equation for our triangle is:
A = √(9*(9-x)*(9-x)*(2x-9))
From this, you can take the derivative to find the critical point and find the maximum area of the triangle and then work backwards to get the dimensions. Can you finish this up on your own?
Donald W.
That's from simplifying (9-(18-2x)). 18-2x is the side length and I'm subtracting that from the semi-perimeter length of 9.04/07/22
Khushi S.
how did you get the (2x-9) for the last side length in the equation?04/07/22