Problem

4. A square with area 54 square units is placed beside a square with area 75 square units. Find the outside perimeter of the given shape, in fully simplified form. (3 marks)

Answer

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Answer

\boxed{perimeter = 6\sqrt{6} + 10\sqrt{3}}

Steps

Step 1 ：Find the side lengths of both squares: \(side_square1 = \sqrt{54} = 3\sqrt{6}\) and \(side_square2 = \sqrt{75} = 5\sqrt{3}\)

Step 2 ：Find the perimeter of the combined shape: \(perimeter = 2(side_square1 + side_square2) = 2(3\sqrt{6} + 5\sqrt{3}) = 6\sqrt{6} + 10\sqrt{3}\)

Step 3 ：\boxed{perimeter = 6\sqrt{6} + 10\sqrt{3}}

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