Question

In a rectangle if
the length is increased & breadth is reduced by 3 cm then area is reduced by 18 cm². If
the length is reduced by I cm & breath is increased
by 2 cm then area is increased by 14cm² ? Actual breadth of the rectangle are respectively​

Answer 1

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

$\sf{\implies The\:actual\:length\:_{(rectangle)}=x}$

$\sf{\implies The\:actual\: breadth\:_{(rectangle)}=y}$

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

$\sf{\implies The\:actual\:length\:and\: breadth\:_{(rectangle)}=?}$

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

• To calculate actual length and breadth of rectangle at first we have to set up equation as per the given clue in the question.

$\sf\small\underline\red{Given\:in\:case\:(i):-}$

• In a rectangle if the length is increased & breadth is reduced by 3 cm then area is reduced by 18 cm².

$\sf\small\underline\purple{Formula\:used:-}$

$\sf\green{\implies Area\:_{(rectangle)}=Length\times\: breadth}$

$\tt{\implies (x+3)(y-3)=x\times\:y-18}$

$\tt{\implies xy+3y-3x-9=xy-18}$

$\tt{\implies 3x-3y=xy-xy-9+18}$

$\tt{\implies 3x-3y=9}$

• Dividing by 3 on both sides:-]

$\tt{\implies x-y=3------(i)}$

$\sf\small\underline\red{Given\:in\:case\:(ii):-}$

• In a rectangle If the length is reduced by I cm & breath is increased by 2 cm then area is increased by 14cm².

$\tt{\implies (x-1)(y+2)=x\times\:y+14}$

$\tt{\implies xy-y+2x-2=xy+14}$

$\tt{\implies 2x-y=xy-xy+14+2}$

$\tt{\implies 2x-y=16-----(ii)}$

• In equation (i) multiplying by 2 then subract from equation (ii):-]

$\tt{\implies 2x-2y=6}$

$\tt{\implies 2x-y=16}$

• by solving we get here:-]

$\tt{\implies -y=-10\implies y=10cm}$

• Putting the value of y=10 in eq (i):-]

$\tt{\implies x-y=3}$

$\tt{\implies x-10=3}$

$\tt{\implies x=3+10}$

$\tt{\implies x=13cm}$

$\sf\large{Hence,}$

$\sf{\implies The\:actual\:length\:_{(rectangle)}=13cm}$

$\sf{\implies The\:actual\: breadth\:_{(rectangle)}=10cm}$

Answer 2

Refer to the above attachment