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 - Mathematics

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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 house can be constructed.

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Solution

Let ABCD is a rectangular plot having a measurement of 40 m long and 15 m front.

∴ Length of inner-rectangle, EF = 40 – 3 – 3 = 34 m and Breadth of inner-rectangle, FG = 15 – 2 – 2 = 11 m

∴ Another rectangle EFGH will be formed inside the rectangle ABCD

∴ Area of innerrectangle, EFGH = Length × Breadth

= EF × FG

= 34 × 11

= 374 m2  ......[∴ Area of a rectangle = length × breadth]

Hence, the largest area where the house can be constructed in 374 m2.

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Chapter 12: Heron's Formula - Exercise 12.4 [Page 119]

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NCERT Exemplar Mathematics Class 9
Chapter 12 Heron's Formula
Exercise 12.4 | Q 4 | Page 119

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