Current location - Plastic Surgery and Aesthetics Network - Plastic surgery and beauty - (20 12? Zhengzhou simulation) As shown in the figure, line segment AB=8cm, point C is any point on AB (not coincident with points A and B), and AC and BC are the same as the hypotenuse in AB.
(20 12? Zhengzhou simulation) As shown in the figure, line segment AB=8cm, point C is any point on AB (not coincident with points A and B), and AC and BC are the same as the hypotenuse in AB.
Solution: MD⊥AC, NE⊥BC,

∫△AMC and△△△ CNB are isosceles right triangles,

∴DC=MD,EB=NE，

Let AC=xcm, then BC=(8-x)cm,

∴ The sum of the areas of two triangles is S= 12? x？ 12x+ 12？ (8-x)？ 12(8 x)

= 14 x2+ 14(64+x2- 16x)

= 14 x2+ 16+ 14 x2-4x

= 12x2-4x+ 16

When AC=-? 42× 12=4,

That is, when BC=8-4=4cm, the areas of the two isosceles triangles are the smallest.

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