question_answer

The lengths of two sides of a right angled triangle which contain the right angle are a and b, respectively. Three squares are drawn on the three sides of the triangle on the outer side. What is the total area of the triangle and the three squares'

A)  \[2\,\,({{a}^{2}}+{{b}^{2}})+ab\]

B)  \[2\,\,({{a}^{2}}+{{b}^{2}})+2.5ab\]

C)  \[2\,\,({{a}^{2}}+{{b}^{2}})+0.5ab\]

D)  \[25\,\,({{a}^{2}}+{{b}^{2}})\]

Correct Answer: C

Solution :

\[\therefore \] Total area \[={{a}^{2}}+{{b}^{2}}(\sqrt{{{({{a}^{2}}+{{b}^{2}})}^{2}}}+\frac{1}{2}ab=2\,\,({{a}^{2}}+{{b}^{2}})+0.5ab\]