If a is the length of the equal sides and b the length of the third side, then 2a+b=7.5, the perimeter. The area is found by splitting the triangle into two congruent right-angled triangles back to back. The common side is the height of the triangle. This height^2=a^2-(b/2)^2 by Pythagoras. The area of the triangle is half the base times the height=(b/2)sqrt(a^2-b^2/4). But b=7.5-2a, so the area=(3.75-a)sqrt(a^2-(56.25-30a+4a^2)/4)=(3.75-a)sqrt(4a^2-56.25+30a-4a^2)/2=(3.75-a)sqrt(30a-56.25)/2. So a must be bigger than 1.875 m, so that 30a>56.25 to make it possible to take the square root and, since b is positive and b=7.5-2a, then 7.5-2a>0 and a<3.75 m. So a is between 1.875 and 3.75 metres. When a=3.075 m the area is 2.025 sq m and b=1.35 m. The height is 3 m. This solution has rational values for all the sides and the height.