Question 1158593
<br>
For a right triangle, the area is half the product of the lengths of the legs.  So the area of this right triangle is 24 cm^2.<br>
The area of any triangle is also one-half the product of the radius of the circle and the perimeter of the triangle: {{{A = (1/2)(p)(r)}}}<br>
The hypotenuse in a right triangle with legs 6cm and 8cm is 10cm; the perimeter is then 24cm.  So<br>
{{{24 = (1/2)(24)(r)}}}
{{{r = 2}}}<br>
ANSWER: The radius of the inscribed circle ("the radius of the largest circle that can be drawn inside the triangle") is 2cm.<br>