Question

The area of a rectangle is 84m². If the length is decreased by 1m and the breadth is increased by 1m, the original area increases by 4m². find the length and breadth of the rectangle.​

Answer 1

SOLUTION :-

Let,

Length = x

Breadth = y

Given,

Area of the rectangle = 84 m²

So,

$\longrightarrow\sf xy = 84$

According to the question,

$\longrightarrow\sf (x-1)(y+1)=xy+4 \\\\\longrightarrow xy+x-y-1=4 \\\\\longrightarrow x-y= 5 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ........................(1)$

We know that,

   $\bf (x+y)^2=(x-y)^2+4xy$

$\longrightarrow\sf (x+y)^2=(x-y)^2+4\times xy\\\\\longrightarrow (x+y)^2=(5)^2+4\times 84 \\\\\longrightarrow (x+y)^2 = 25+336 \\\\\longrightarrow (x+y)^2=361 \\\\\longrightarrow x+y=\sqrt{361} \\\\\longrightarrow x+y = 19 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .......................(2)$

Equation (2) + Equation (1),

$\longrightarrow\sf 2x=24\\\\\longrightarrow \bf x = 12$

Substitute x = 12 in equation (1),

$\longrightarrow\sf 12+y = 19 \\\\\longrightarrow\bf y = 7$

Length of the rectangle = 12 m

Breadth of the rectangle = 7 m

Answer 2

Answer:

length of rectangle = 12m

breath of rectangle = 7m

Step-by-step explanation:

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