Mr Palmer bought 36 metres of barbed wire to make a fence for a garden. The plot of land is rectangular in shape. Assuming that the length and width are to be whole numbers, answer the following:
(i) List the possible dimensions that the garden could have.
(ii) For each set of dimensions, find the area that the garden would enclose
(iii) Which dimensions give the greatest area?
(iv) What is the greatest area?
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Let the length of rectangular garden is l and breadth is b.
A/c to question, Garden is fenced on three sides.
∴ l + 2b = 30
l = 30 - 2b ------(1)
Given, area of rectangular garden = 100 m²
l × b = 100
(30 - 2b)b = 100
30b - 2b² = 100
2b² - 30b + 100 = 0
b² - 15b + 50 = 0
b² - 10b - 5b + 50 = 0
(b - 10)(b - 5) = 0
b = 5 and 10
So, l = 30 - 2b ⇒l = 20 or 10
Hence, rectangular garden sides (20, 5) or (10, 10)
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