Question

The length of rec tagle exceeds it's breath by 7cm .If the length is decreased by 4cm and the breath is increased by 3cm,the area of the new rectangle is the same as the area of the original rectangle .Find the length and breath of the original rectangle.​

Answer 1

$\sf\large\underline{Let:}$

$\rm{\implies Rectangle\:_{(length)}=x}$

$\rm{\implies Rectangle\:_{(breadth)}=y}$

$\rm{\implies Rectangle\:_{(orginal\:area)}=xy}$

$\sf\large\underline{To\: Find:}$

$\rm{\implies Rectangle\:_{(length\:and\: breadth)}=?}$

$\sf\large\underline{Solution:}$

• At first we have to set up the equation according to given clue in the question than solve the equation.]

$\sf\small\underline{Given\:in\: Case\:(i):}$

• The length of rectangle exceeds it's breath by 7cm]

$\rm{\implies x=y+7------(i)}$

$\sf\small\underline{Given\:in\: Case\:(ii):}$

• The length is decreased by 4cm and the breath is increased by 3cm,the area of the new rectangle is the same as the area of the original rectangle.]

$\rm{\implies Area\:_{(new\: rectangle)}=Area\:_{(original\: rectangle)}}$

$\rm{\implies (x-4)(y+3)=xy}$

$\rm{\implies xy+3x-4y-12=xy}$

$\rm{\implies 3x-4y=xy-xy+12}$

$\rm{\implies 3x-4y=12------(ii)}$

• Now, putting the value x=y+7 in eq (ii)

$\rm{\implies 3x-4y=12}$

$\rm{\implies 3(y+7)-4y=12}$

$\rm{\implies 3y+21-4y=12}$

$\rm{\implies 3y-4y=12-21}$

$\rm{\implies -y=-9\implies y=9cm}$

• Now putting the value of y=9 in eq (i)

$\rm{\implies x=y+7}$

$\rm{\implies x=9+7\implies x=16cm}$

$\sf\large{Hence,}$

$\rm{\implies Length\:_{(orginal\: rectangle)}=16cm}$

$\rm{\implies Breadth\:_{(orginal\: rectangle)}=9cm}$

Answer 2

Let:

length=x

breadth=y

Area=xy

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

(x-4)(y+3)=xy

xy+3x-4y-12=xy

3x-4y=12

putting value here

3(y+7)-4y=12

3y+21-4y=12

-y=-9

y=9

putting the value of y=9 eq 1

x=y+7

x=9+7

x=16

so,

length=16

breadth=9