GATE Civil Engineering (CE) 2019 Shift 1 Solved Paper

Question : 7 of 65

Marks: +1, -0

A square has sides

5 {cm}

smaller than the sides of a second square. The area of the larger square is four times the area of the smaller square. The side of the larger square is

{cm}

$15.10$
$18.50$
$10.00$
$8.50$

Validate

Solution:

\;\text " Given, "\;

\;\text " (Area) "\;_{ {B}}=4 ×(\;\text " Area "\;)_{ {A}}

⇒ x^{2}=4(x-5)^{2}

⇒ x^{2}=4[x^{2}+25-10 x]

⇒ x^{2}=4 x^{2}+100-40 x

⇒ 3 {x}^{2}-40 {x}+100=0

⇒ 3 x^{2}-30 x-10 x+100=0

⇒ 3 x(x-10)-10(x-10)=0

⇒ x=10 \;\text " or "\; x=\;{10}/{7}

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