A rectangular plot is given for constructing a house, having a measurement of $40 m$ long and 15 m in the front. According to the laws, a minimum of $3 m$ , wide space should be left in the front and back each and $2 m$ wide space on each of other sides. Find the largest area where the house can be constructed.

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Solution

$L e t t h e p l o t b e r e c t a n g l e A B C D w h e r e l e n g t h A D = B C = 40 m & w i d t h A B = C D = 15 m . E f f e c t i v e l e n g t h o f p l o t a f t e r l e a v i n g 3 m e a c h i n t h e f r o n t a n d b a c k = E H = F G = 40 - (3 + 3) = 34 m E f f e c t i v e w i d t h o f p l o t a f t e r l e a v i n g 2 m e a c h o n t h e s i d e s = E F = H G = 15 - (2 + 2) = 11 m ∴ T h e l a r g e s t a r e a w h e r e t h e h o u s e c a n b e c o n s t r u c t e d = A r e a o f r e c t a n g l e E F G H = E H \times H G = 34 \times 11 = 374$

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