Question

perimeter of
A rectangular plot is 42 metre and area is
108 m²
1.taking x as the length of the plot write down breath in terms of X
2. Find the area of plot in terms of X hence make a equation
3. Solve the equation and find the dimensions of the plot​

Answer 1

✪AnSwEr

${\tt{\red{\underline{\large{Given}}}}}$

• A rectangular plot
• Of area = 108m²
• and Perimeter =52 m

${\sf{\green{\underline{\large{To\:find}}}}}$

• .1taking x as the length of the plot write down breath in terms of X

• 2. Find the area of plot in terms of X hence make a equation

• 3. Solve the equation and find the dimensions of the plot

${\sf{\pink{\underline{\Large{Explanation}}}}}$

Diagram

$\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\thicklines\put(8.6,3){\large{P}}\put(7.7,0.9){\large{Q}}\put(9.5,0.7){\sf{\large{Breadth}}}\put(11.1,0.9){\large{R}}\put(8,1){\line(1,0){3}}\put(11,1){\line(1,2){1}}\put(9,3){\line(3,0){3}}\put(7.7,2){\large{ \sf\:Length }}\put(8,1){\line(1,2){1}}\put(12.1,3){\large{S}}\put(8,1){\line(2,1){4}}\put(11,1){\line(-1,1){2}}\end{picture}$

Let the length of the plot be x

Then

Breadth = ?

• Perimeter of Rectangle = 2(L+B)

=>2(L+B)=42

=>L+B=21

=>X+B=21

=>B=21-X

According to the question

• Area = 108m²

Area of Rectangle = Length × Breadth

=>X(21-X)=108

=>-x²+21x-108=0

=>x²-21x+108=0

=>X²-12x-9x+108=0

=>x(x-12)-9(X-12)=0

=>(X-12) (X-9)

x=12,9

Here

First case

• L=12

• B=(21-12)

• B=9

Second Case

• L=9

• B=(21-9)

• B=12

Hence the dimensions of Rectangle is 12 and 9