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in Mathematics by (66.0k points)

The area of each of the four congruent L-shaped regions of this 100 cm by 100 cm square is 3/16 of the total area. How many centimeters long is the side of the centre square ?

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Area of outer square = 100 × 100 = 10000 cm2

Area of L-shaped region = 3 × 625 = 1875 cm2

Area of 4 L-shaped region 4 × 1875 = 7500 cm2

Area of centre square = 10000 – 7500 cm2 = 2500

Side of centre square = √2500 = 50 cm.

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