SSC CGL 10 Aug 2017 Shift 1 Paper

Question : 67 of 100

Marks: +1, -0

Smaller diagonal of a rhombus is equal to length of its sides. If length of each side is 4 cm, then what is the area (in cm

^{2}

) of an equilateral triangle with side equal to the bigger diagonal of the rhombus?

Solution:

a = 4 cm,

d_1

= 4 cm

⇒

a=1/2√{d_1^2+d_2^2}

⇒

4=1/2√{(4)^2+d_2^2}

⇒

8=√{16+d_2^2}

On squaring both sides,

64 = 16 + d_2^2

⇒

d_2^2=48

∴

d_2=4√3

Area of equilateral triangle

=√3/4×(4√3)^2=12√3\cm^2

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