Question

the length of a rectangle exceeds its breath by 7cm. if the length is decreased by 4cm and the breath is increased by 3cm. the are of the new rectangale is same as the area of the origial rectangle. find length and breath

Answer 1

Answer:

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

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

Step-by-step Explanation:

$\bf\large{\underline{Assume:}}$

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

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

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

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

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

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

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

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

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

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

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

• 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.

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

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

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

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

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

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

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

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

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

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

$\sf{\implies{-y=-9}}$

$\implies {y=9cm}$

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

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

$\sf{\implies x=9+7}$

$\sf\implies{x=16cm}$

$\bf\large{Hence,}$

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

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

Answer 2

ʟᴇɴɢᴛʜ=16ᴄᴍ

ʙʀᴇᴀᴅᴛʜ=19 ᴄᴍ