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 houses can be constructed.

Solution:

Given, a rectangular plot for constructing a house

The dimension of the plot is 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 the other sides.

We have to find the largest area where houses can be constructed.

Let ABCD be the rectangular plot

AB = CD = 40 m

BC = AD = 15 m

Let the inner rectangle be EFGH

EF = GH = 40 - 3 - 3

So, EF = GH = 34 cm

EH = FG = 15 - 2 - 2

So, EH = FG = 11 cm

The largest area to construct the house = area of rectangle EFGH

Area of rectangle = length × breadth

Area of rectangle EFGH = EF × GH

= 34 × 11

= 374 cm²

Therefore, the largest area where the house can be constructed is 374 cm²

✦ Try This: A rectangular plot is given for constructing a house, having a measurement of 50 m long and 18 m in the front. According to the laws, a minimum of 2 m, wide space should be left in the front and back each and 1 m wide space on each of the other sides. Find the largest area where houses can be constructed.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 12

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NCERT Exemplar Class 9 Maths Exercise 12.4 Problem 4

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 houses can be constructed.

Summary:

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 the other sides. The largest area where houses can be constructed is 374 cm²

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