To find: The function that models the area A in terms of length of its base b of an isosceles triangle.
The function that model the area of isosceles triangle is .
The isosceles triangle is shown below.
Area of triangle is given by,
As shown in Figure 1 height is y and base is b.
Perimeter P of triangle shown in Figure 1 is,
Substitute in above equation to get x in terms of b.
Apply Pythagorean Theorem in triangle
Substitute , and in above equation.
Substitute in above equation and get y in terms of b.
Take square root of above equation.
Substitute for y in equation (1)
Thus, the function that model the area of isosceles triangle is .
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