The diagonal of a rectangle is √(41) cm and its area is 20 sq. cm. The perimeter of the rectangle must be

ABC26GN4334 · Area

Subject: General Aptitude · Chapter: Area · Exam: 2002 · Marks: · Difficulty:

The diagonal of a rectangle is $\sqrt{41} \mathrm{cm}$ and its area is 20 sq. cm. The perimeter of the rectangle must be

(a)9 cm

(b)18 cm

(c)20 cm

(d)41 cm

Answer

Answer (as printed):

Explanation

$\sqrt{l^{2}+b^{2}}=\sqrt{41}$ or $l^{2}+b^{2}=41$. Also, $l b=20$. $$(l+b)^{2}=\left(l^{2}+b^{2}\right)+2 l b=41+40=81 \Rightarrow(l+b)=9 .$$ ∴ Perimeter $=2(l+b)=18 \mathrm{cm}$.

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