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Question 59
The diagonal of a square is 10 cm. What will be the length of the diagonal of the square whose area is double of the area of first square?
Solution
Given, Diagonal of a square = 10 cm
$$\sqrt{2}a = 10 => a = \dfrac{10}{\sqrt{2}} cm$$
Area of the square = $$(Â \dfrac{10}{\sqrt{2}} )^2 = \dfrac{100}{2} = 50 cm^2$$
Area of new square = $$2\times50 = 100 cm^2$$
Then, Side of new square = $$\sqrt{100} = 10 cm$$
Therefore, Diagonal of the new square = $$\sqrt{2} \times 10 = 10\sqrt{2} cm$$
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