A right-angled triangle ABC is inscribed in a semi-circle of radius 1cm, with one of its non-hypotenuse side AB lying on the diameter. Find the largest possible area of triangle ABC.
A right-angled triangle ABC is inscribed in a semi-circle of radius 1cm, with one of its non-hypotenuse side AB lying on the diameter. Find the largest possible area of triangle ABC.
Umm Skeeter I think you have misinterpreted the problem. The non hypotenuse side of the triangle is on the diameter, but it cannot be the diameter, or else the triangle will not be right-angled.
my mistake ...
consider the graph of the semicircle of radius 1 centered at the origin
$\displaystyle y = \sqrt{1 - x^2}$
base of triangle = $\displaystyle 1 + x$
height of triangle = $\displaystyle y = \sqrt{1 - x^2}$
$\displaystyle A = \frac{1}{2}(1+x)\sqrt{1-x^2}$
Not knowing what your background is, either graph the area function in your calculator to find the maximum, or use calculus to optimize the area.