Question

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

Answer 1

Given

Rectangular plot with length $=40cm$ and breadth $=15cm$

$3m$ wide space is left in the front and back each and $2m$ wide space on each of other sides

Find out

We have to determine the largest area where the house can be constructed

Solution

Let the given rectangle be rectangle PQRS,

According to the given details

PQ $=$ $40m$ and QR $=15m$

As $3m$ is left in both front and back,

AB $=$ PQ $-3-3$

$\Rightarrow$ AB $=40-6$

$\Rightarrow$AB $=$ $34m$

and $2m$ has to be left at both the sides,

BC $=$ QR $-2-2$

$\Rightarrow$ BC $=$$15-4$

$\Rightarrow$ BC $=11m$

Now, Area left for house construction is area of ABCD.

Hence,

Area(ABCD) $=$ AB × CD

$$\begin{gathered} =34\times 11 \\ =374m^2 \end{gathered}$$

Therefore, the largest area where the house can be constructed$374m^2$