155264

12 units:

g) a+b+c=12

c) a+b=12-c

a) Squaring both sides= a²+2ab+b²=144-24c+c²

f) By Pythagoras' Theorem, a²+b²=c²

d) So 2ab=144-24c

h) Dividing by 2: ab=72-12c

e) Area of the triangle= ab/2

b) So area of the triangle=36-6c

30 units:

1. a+b+c=30

2. a+b=30-c

3. Squaring both sides: a²+2ab+b²=900-60c+c²

4. Pythagoras' theorem: 2ab=900-60c

5. Dividing by 2: ab=450-30c

6. Area of the triangle=ab/2

7. So area of the triangle=225-15c

Extension

1. a+b+c=p

2. a+b=p-c

3. Squaring both sides: a²+2ab+b²=p²-2pc+c²

4. Pythagoras' theorem, a²+b²=c²

5. So 2ab=p²-2pc

6. Dividing by 2: ab=p²/2-pc

7. Area of the triangle=ab/2

8. p²/4-pc/2