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If the length of a diagonal of a square is (a + b), then the area of the square is:
Answer & Solution
Correct Answer:
Option
B
Diagonal of a square = (a + b)
∴ side of square = $$\frac{{\left( {a + b} \right)}}{{\sqrt 2 }}$$
∴ Area of square = (side)2
$$\eqalign{ & = {\left( {\frac{{a + b}}{{\sqrt 2 }}} \right)^2} \cr & = \frac{1}{2}\left( {{a^2} + {b^2} + 2ab} \right) \cr & = \frac{1}{2}\left( {{a^2} + {b^2}} \right) + ab \cr} $$
∴ side of square = $$\frac{{\left( {a + b} \right)}}{{\sqrt 2 }}$$
∴ Area of square = (side)2
$$\eqalign{ & = {\left( {\frac{{a + b}}{{\sqrt 2 }}} \right)^2} \cr & = \frac{1}{2}\left( {{a^2} + {b^2} + 2ab} \right) \cr & = \frac{1}{2}\left( {{a^2} + {b^2}} \right) + ab \cr} $$
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