Question

Suppose an isosceles triangle has perimeter 10 cm. Find an expression for its area A as a function of the
length of its base b (assume that the other two sides are the sides of equal length). What is the domain
of A?

Answer 1

let each of the equal sides be x
so 2x + b = 10
x = (10-b)/2

let the height be h
h^2 + (b/2)^2 = [(10-b)/2]^2
h^2 + b^2/4 = (100 - 20b + b^2)/4
h^2 = (100-20b+b^2-b^2)/4
h^2= (100-20b)/4
h = √(100-20b)/2

area = (1/2)bh
= (1/2)b(√(100-20b)/2
= (1/4) b√(100-20b)

check my arithmetic