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Question

# Sketch the figure that is described. Find the requested length. Round decimals to the nearest tenth. The diagonal of a square is 26 inches. Find the length of a side.

Solution

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Let's remember that the diagonal of any square divides into two congruent isosceles right triangles by the diagonal, where this diagonal will be a common hypotenuse for these two triangles.

The graph below describes the given conditions as follows: The diagonal $AC$ divides each of the right angles $\angle BAD$ and $\angle BCD$ into two equal angles, then

$\alpha=\angle BAC=45^{\circ}$

Notice that the side length of the given square is the leg of the isosceles right triangles.

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