question_answer

The lengths of the sides of a triangle are 5m, \[1.2\]decametre and 130 dm. Then its area is ____.

A)  \[24\,{{m}^{2}}\]                           

B)  \[30\,{{m}^{2}}\]   

C)  \[48\,{{m}^{2}}\]               

D)         \[40\,{{m}^{2}}\]   

Correct Answer: B

Solution :

        Let \[BC=1.2\]decameter = 12 m          \[AC=130\,dm=\frac{130}{10}m=13\,m\]                         and \[AB=5\text{ }m\]                 Now, it is clear that,     \[A{{B}^{2}}+B{{C}^{2}}=A{{C}^{2}}\]         So, it is a right angled triangle.           \[\therefore \] Area \[=\frac{1}{2}\times BC\times AB=\frac{1}{2}\times 12\times 5=30\,{{m}^{2}}\]