SOLUTION: What are the dimensions of a rectangle with an area of 81 sq. cm and a perimeter of 60 cm?
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Question 1036169: What are the dimensions of a rectangle with an area of 81 sq. cm and a perimeter of 60 cm?
Answer by Cromlix(4381) (Show Source): You can put this solution on YOUR website!
Hi there,
a rectangle with an area of 81 sq.
Area of rectangle = length x width
l x b = 81
l = 81/w
Perimeter of rectangle = 2 x length + 2 x width
60 = 2(81/w) + 2 x width
60 = 162/w + 2w
Multiply through by w
60w = 162 + 2w^2
Sort into ax^2 + bx + c = 0 form
2w^2 - 60w + 162 = 0
Divide by 2
w^2 - 30w + 81 = 0
Factorize
(w - 3)(w - 27) = 0
w = 3 or 27
Using l = 81/w
If w = 3cms then l = 27cms
If w = 27cms then l = 3cms
Hope this helps :-)
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