A red square is drawn in one corner of a rectangle so that it just fits under the diagonal as shown in the diagram.

If the rectangle has dimensions 10cm and 15cm find the area of the square.

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Let the length of the square be x centimetres.

Consider the corresponding lengths of the smaller sides of the two orange triangles.

\(\frac{10-x}{x} = \frac{x}{15-x}\)

Solving this equation gives x = 6

So the area of the red square is 36cm^{2}

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