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A triangle has perimeter 32 cm, one side is 11 cm and difference of other two sides is 5 cm. Determine its area.

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A triangle has perimeter 32 cm, one side is 11 cm and difference of other two sides is 5 cm. Determine its area. 

(a) 4 √30cm (b) 8 √30cm (c) 6 √30cm (d) 5 √30cm

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(b) Let a, b and c be the three sides of ΔABC. 

Given a = 11 cm 

and a + b + c = 32 cm 

11 + b + c = 32 cm 

b + c = 21 cm       ----(1) 

Also, we are given that 

b – c = 5 cm       ----(2) 

Adding (1) and (2) 

2b = 26 cm 

b = 13 cm and c = 8 cm

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