Question

The length of rectangle is thrice ti Breadth. If the length is decrease 9 and breadth is increase 9. If the area Increase 81 sq cm. Then what is length

Answer 1

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$  

Assumption

Let the breadth be p

Also,

Length be 3p

Length is decreased by 9cm

= 3p - 9 cm

Also,

Breadth = p + 9 cm

Here we have to apply,

Area of rectangle = Lenght × Breadth

(3p - 9)(p + 9) - 3p × p = 81

3p² + 27p - 9p - 81 - 3p² = 81

18p - 81 = 81

18p = 162

p = 162/18

p = 9 cm

Hence,

Breadth = 9 cm

Length = 3p

= 3 × 9

= 27 cm

${\boxed{\bigstar{{Length = 27cm\:and\:Breadth=9cm}}}}$          

Answer 2

Question :

The length of rectangle is thrice of its Breadth. If the length is decrease 9cm and breadth is increase 9cm . If the area Increase 81 sq cm. Then what is length ?

Solution :

Let the Breadth of rectangle be x .

⇒Length of rectangle be 3 x

Diagram :.

$\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\thicklines\put(7.7,3){\large{A}}\put(7.5,2){\large{ \sf\:x }}\put(7.7,1){\large{B}}\put(9.5,0.7){\sf{\large{3x}}}\put(11.1,1){\large{C}}\put(8,1){\line(1,0){3}}\put(8,1){\line(0,2){2}}\put(11,1){\line(0,3){2}}\put(8,3){\line(3,0){3}}\put(11.1,3){\large{D}}\end{picture}$

$\rule{150}{1}$

According to the question:

If the length is decrease 9cm and breadth is increase 9cm. Then the area Increase is 81 sq cm.

⇒ length ,l' = 3x-9

and breadth , b' = x+9

We know that ,

area of a rectangle = length × breadth

⇒Increase in Area = 81 sq cm

$\sf \implies(3x - 9)(x + 9) - 3x \times x = 81cm {}^{2}$

$\implies \sf3x {}^{2} + 27x - 9x - 81 - 3x {}^{2} = 81$

$\sf \implies18x - 81 = 81$

$\sf \implies18x = 162$

$\sf \implies \: x = \frac{ \cancel{162}}{ \cancel{18}} = 9$

Therefore,

Breadth ,x = 9 cm

and Length = 3x= 3× 9= 27 cm