Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
If the length of a certain rectangle is decreased by 4 cm and the width is increased by 3 cm, a square with the same area as the original rectangle would result. The perimeter of the original rectangle (in cm) is
(a)44
(b)46
(c)48
(d)50
Answer
Answer (as printed): D
Explanation
Let the length and width of the rectangle be $l \mathrm{cm}$ and $b$ cm respectively. Then, $(l-4)(b+3)=l b \Rightarrow l b+3 l-4 b-12=l b$ $$\Rightarrow 3 l-4 b=12$$ And, $l-4=b+3 \Rightarrow l-b=7$ Multiplying (ii) by 4 and subtracting (i) from it, we get : $l=16$. Putting $l=16$ in (ii), we get : $b=9$. ∴ Perimeter of the original rectangle $$=2(l+b)=[2(16+9)] \mathrm{cm}=50 \mathrm{cm} .$$