Question

the area of a rectangle field is 1440 sq meter and perimeter is 152 meter .out of length or breadth which one is to be decreased by what percentage to make a square?why?find it.

Answer 1

Answer:

If Length is decreased by 10% then it would become a square.

Step-by-step explanation:

Given:

Area of Rectangular field = 1440 sq. m

Perimeter = 152 m.

We need to find which one needs to be decreased by what percentage to make it a square.

Solution:

Let length be denoted by 'l'.

Also Let width be denoted by 'w'.

Now we know that Area of rectangular field is given by Length times width.

framing in equation form we get;

l\times w = 1440 \ \ \ \ equation\ 1l×w=1440 equation 1

Also we know that Perimeter of rectangular field is given by 2 times sum of Length and width.

framing in equation form we get;

\begin{gathered}2(l+w) =152\\\\l+w =\frac{152}{2}\\\\l+w=76\\\\l=76-w \ \ \ \ equation \ 2\end{gathered}

2(l+w)=152

l+w=

2

152

l+w=76

l=76−w equation 2

Now Substituting equation 2 in equation 1 we get;

\begin{gathered}l\times w =1440\\\\(76-w)w=1440\\\\76w-w^2=1440\\\\w^2-76w+1440 =0\end{gathered}

l×w=1440

(76−w)w=1440

76w−w

2

=1440

w

2

−76w+1440=0

Now we will find the root by factorizing the same we get;

\begin{gathered}w^2-36w-40w+1440=0\\\\w(w-36)-40(w-36)=0\\\\(w-36)(w-40) =0 \\\end{gathered}

w

2

−36w−40w+1440=0

w(w−36)−40(w−36)=0

(w−36)(w−40)=0

Now solving for each to find the value of 'w' we get;

\begin{gathered}w-36 =0\\\\w=36\\\\also \\\\w-40=0\\\\w=40\end{gathered}

w−36=0

w=36

also

w−40=0

w=40

So We can say that;

Width = 36 m and Length = 40 m

Now we need to find out of length or breadth which one is to be decreased by what percentage to make it a square.

We know that square has all sides same.

So from the data we found we can say that if length is decreased by 4 then length and breadth(width) both will be equal.

So to find percentage decreased we will divide length to be decreased by total length and then multiply by 100.

framing in equation form we get;

percentage decreased = \frac{4}{40}\times 100 = 10\%

40

4

×100=10%

Hence If Length is decreased by 10% then it would become a square.