Question

Length of a rectangular field is increased by $7cm$ and breadth is decreased by $3cm$, area of the field remains unchanged. If length be decreased by $7cm$ and bhreadth be increased by $5cm$,again area remains unchanged. Find the length and breadth of the rectangular field

• A. $26cm12cm$
• B. $28cm15cm$
• C. $30cm16cm$
• D. $18cm12cm$

Answer 1

Answer: (B)

$28cm15cm$

Let length and breadth be l and b

$l\times b=a\to 1$

Given $(l+7)(b-3)=a\to 2$

Given $(l-7)(b+5)=a\to 3$

Dividing equations $1/2$

$l\times b=(l+7)(b-3)$

$lb=lb-3l+7b-21$

$3l-7b=-21\to 1$

Dividing equations $1/3$

$lb=(l-7)(b+5)$

$lb=lb+5l-7b-35$

$5l-7b=35\to 2$

$1-2$

$3l-7b=-21$

$5l-7b=35$

$-+-$

$-2l=-56$

$l=28$

$3\left(28\right)-7b=-21$

$7b=84+21=105$

$b=15$

$\therefore l=28$ & $b=15$