Aright triangle has an area 18 square inches.
a: if the triangle is an isosceles triangle, what are the lengths of the legs of the triangle

The area of any triangle is             A = (1/2) (base) (height).

If the right triangle is not sitting
on its hypotenuse, then one leg
is the base, and the other leg is
the height:                                      A = (1/2) (base leg) (height leg) .

If the triangle is isosceles, then
the legs are equal:                        A = (1/2) (either leg)²

You said the area is 18 in²:          18 in² = (1/2) (leg²)

Multiply each side by 2 :              36 in²  =  leg²

Square root each side:                  6 in   =  leg