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Differentiate a triangle constrained to fixed area

The right-angled triangle ABCABC has AB=cAB=c cm, BC=aBC=a cm and AC=bAC=b cm, with right angle at CC and fixed area 100 cm2100\text{ cm}^2.

Express bb in terms of aa. Given that BCBC increases at 3 cm s−13\text{ cm s}^{-1}, find the rate of change of cc when a=20a=20.

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Right-angled triangle ABC with A at the left, C at the lower right and B above C. The horizontal leg AC is b cm, vertical leg BC is a cm and hypotenuse AB is c cm; angle C is a right angle.
Right-angled triangle ABC with A at the left, C at the lower right and B above C. The horizontal leg AC is b cm, vertical leg BC is a cm and hypotenuse AB is c cm; angle C is a right angle.
Right-angled triangle ABC with A at the left, C at the lower right and B above C. The horizontal leg AC is b cm, vertical leg BC is a cm and hypotenuse AB is c cm; angle C is a right angle.

[2018/VJC/I/10(b)]

CJC · Discussion · Question 10

Use the area constraint before differentiating the hypotenuse.

Read the worked solution