Question

The length of a rectangle exceeds its breadth by 7 cm. If the length is decreased by 4 cm and the breadth is increased by 3 cm, the area of the new rectangle is the same as the area of the
original rectangle. Find the length and the breadth of the original rectangle. ​

Answer 1

Answer:

The length of the rectangle is 16cm

and the breadth is 9cm

Step-by-step explanation:

Let the length and breadth of the rectangle be x and y respectively

Therefore ,

Area of the rectangle is = xy

Given , length exceeds its breadth by 7cm

x = y + 7 -----(1)

Again , According to Question

$(x - 4)(y + 3) = xy \\ \implies \: xy + 3x - 4y - 12 = xy \\ \implies 3x - 4y - 12 = xy - xy \\ \implies3x - 4y - 12= 0 \\ \implies 3x - 4y = 12 - - - (2)$

Now , using the value of 'x' from (1) in (2) we have

$3(y + 7) - 4y = 12 \\ \implies3y + 21 - 4y = 12 \\ \implies - y = 12 - 21 \\ \implies - y = - 9 \\ \implies \: y = 9$

Now , from (1) we have

$x = 9 + 7 \\ \implies \: x = 16$

Therefore , required length of the rectangle is 16cm and breadth is 9cm

Answer 2

Answer :

The length of the rectangle is 16 cm.

The breadth is 9 cm.

Step-by-step explanation :

Given that :

The length of a rectangle exceeds its breadth by 7 cm.

To Find :

The length and the breadth of the original rectangle. ​

Solution :

Let the length and breadth of the rectangle be x and x + 7.

So, Area will be "x(x + 7)"

According to your question :

$\sf (x+7-4)(x+3) = x(x+7)\\\\\implies (x+3) (x+3) = x^2+7x\\\\\implies (x+3)^2 = x^2 + 7\\\\\implies x^2 + 9 + 6x = x^2+7x\quad(Here\;x^2\;and\;x^2 are\; cancelled.)\\\\\implies 6x-7x = - 9\\\\\implies -x = -9\quad(Here\; sign\; of\; minus(-)\;is\;cancelled.)\\\\\implies x = 9\\\\\implies Length = 9=7 = 16.\\\\\\\bigstar\;\textbf{\underline{\underline{Hence,The Length is 16cm and Breadth is 9cm. }}}$