A flower chain of length 48 cm is used to form the entrance of a model building. The entrance is in rectangular shape and both ends of the flower chain touch the horizontal ground. Example 3.18 (a) Find the maximum area of the entrance. entrance (b) (i) EXplain (ii) If the height of the entrance must be greater than the width, explain briefly whether the area of the entrance can attain its maximum in (a). Find the width of the entrance when its area is a maximum. ground

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 17EQ
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A flower chain of length 48 cm is used to form the entrance of a model
building. The entrance is in rectangular shape and both ends of the
flower chain touch the horizontal ground.
Example 3.18
(a) Find the maximum area of the entrance.
entrance
(b) (i)
EXplale
(ii) If the height of the entrance must be greater than the width,
explain briefly whether the area of the entrance can attain its
maximum in (a).
Find the width of the entrance when its area is a maximum.
ground
The figure shows a right-angled triangle ABC, where AB = 8 cm and
BC = 12 cm. A rectangle BDEF is inscribed in the triangle. Suppose
40.
DE = x cm.
E
8 cm F
(a) Express the length of EF in terms of x.
x сm
(b) Express the area of rectangle BDEF in terms of x.
12 cm
(c) Find the dimensions and the area of the largest rectangle that can
be inscribed in AABC.
Transcribed Image Text:A flower chain of length 48 cm is used to form the entrance of a model building. The entrance is in rectangular shape and both ends of the flower chain touch the horizontal ground. Example 3.18 (a) Find the maximum area of the entrance. entrance (b) (i) EXplale (ii) If the height of the entrance must be greater than the width, explain briefly whether the area of the entrance can attain its maximum in (a). Find the width of the entrance when its area is a maximum. ground The figure shows a right-angled triangle ABC, where AB = 8 cm and BC = 12 cm. A rectangle BDEF is inscribed in the triangle. Suppose 40. DE = x cm. E 8 cm F (a) Express the length of EF in terms of x. x сm (b) Express the area of rectangle BDEF in terms of x. 12 cm (c) Find the dimensions and the area of the largest rectangle that can be inscribed in AABC.
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