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Four isosceles triangles are formed when both diagonals are drawn in a square. If the length of each side in the square is 8 , what are the lengths of the legs of the isosceles triangles? a (ssqrt2)/(4) b (2ssqrt3)/(2) Need a Hint? c (ssqrt2)/(2)

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Corey

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Answer

C

Explanation

In a square, the diagonals are equal in length and bisect each other at right angles. Therefore, each diagonal divides the square into two congruent isosceles right triangles. The length of each diagonal is given by the Pythagorean theorem as s\sqrt{2}, where s is the side length of the square. Since the diagonal is the hypotenuse of the isosceles right triangle, the length of each leg of the isosceles triangle is given by \frac{s\sqrt{2}}{2}.

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