Math  /  Geometry

QuestionA rectangle has a perimeter of 40 cm and a length of x cmx \mathrm{~cm}. Show that its area is given by A=20xx2A=20 x-x^{2} and find the length when the area is
Xem 96 cm296 \mathrm{~cm}^{2}. P=40 cmP=40 \mathrm{~cm} A=96 cmA=96 \mathrm{~cm}

Studdy Solution
Verify the solutions by substituting x=12 x = 12 and x=8 x = 8 back into the area formula A=20xx2 A = 20x - x^2 :
For x=12 x = 12 : A=20(12)122 A = 20(12) - 12^2 A=240144 A = 240 - 144 A=96cm2 A = 96 \, \text{cm}^2
For x=8 x = 8 : A=20(8)82 A = 20(8) - 8^2 A=16064 A = 160 - 64 A=96cm2 A = 96 \, \text{cm}^2
Both values satisfy the area requirement.
The length x x when the area is 96 96 cm2^2 can be either 12 12 cm or 8 8 cm.

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