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How do you prove that A equals 25-r-5r-5 when a sector of a circle has a perimeter of 20cm and a area of A and the circle has a radius of r?
Wiki User
∙ 11y ago
A=25-(r-5)(r-5)
→
10-r2
(Length of Arc) + (2*radius) = Perimeter of Sector→rӨ+2r=20
so Length of Arc,rӨ=20-2r
Area of sector=½rӨ=rӨ(½r)
Sub length of arc equation into area of sector equation gives: (20-2r)(½r)=10-r2
Thus it is proved.
Wiki User
∙ 11y ago
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