SSC CHSL 13 Apr 2021 Shift 3 Paper

Section: Quantitative Aptitude

Question : 53 of 100

Marks: +1, -0

The perimeter and the area of a rectangular sheet are

42 {m}

and 108

{m}^{2}

, respectively. The length of the diagonal is

Solution:

Let the length and breadth of the rectangular sheet be

x

mand

y {m}

respectively

Given,

2(x+y)=42

and

x+y \;\; =21

. . . (i)

x × y \;\; =108

y \;\; =\;{108}/{x}

⇒ \;\; y=\;{108}/{x}

Put this value in Eq. (i),

\;\;\; x+\;{108}/{x}=21

⇒ \;\; x^{2}-21 x+108=0

⇒ x^{2}-12 x-9 x+108=0

⇒ x(x-12)-9(x-12)=0

∴ \;\; \;\; x=9 \;\text " and "\; 12

\;\text " and "\; y=12 \;\text ", and "\; 9 \;\; [ ∵ \;\text " from Eq. (i)] "\;

∴ \;\text " Length of the diagonal "\;

B D \;\; =√{(D C)^{2}+(B C)^{2}}

\;\; =√{(12)^{2}+(9)^{2}}=√{144+81}

\;\; =√{225}=15 {m}

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