A square and an equilateral triangle have equal perimeters. If the diagonal of the square is 12sqrt{2}text{cm}, then area of the triangle is:

Q: A square and an equilateral triangle have equal perimeters. If the diagonal of the square is $12\sqrt{2}\text{cm},$ then area of the triangle is:

If side of a square is a $cm$ Then, its diagonal $=\sqrt{2}\text{a}\text{cm}$ But diagonal $=12\sqrt{2}\text{cm}$ $\Rightarrow\sqrt{2}\text{a}=12\sqrt{2}$ $\Rightarrow a = 12cm$ $\Rightarrow $ Perimeter of a square $= 4a = 4 \times 12 = 48\ cm$ Now, perimeter of an equilateral triangle with side $x = 3x\ cm$ But perimeter of equilateral triangle = Perimeter of square $\Rightarrow 3x = 48$ $\Rightarrow x = 16\ cm$ Now, Area of equilateral $\triangle=\frac{\sqrt{3}\text{x}^2}{4}=\frac{\sqrt{3}}{4}\times16\times16=64\sqrt{3}\text{cm}^2$ Hence, correct option is $(d)$.

M.C.Q

GSEB - English Medium

A square and an equilateral triangle have equal perimeters. If the diagonal of the square is $12\sqrt{2}\text{cm},$ then area of the triangle is:

A$24\sqrt{2}\text{cm}^2$
B$24\sqrt{3}\text{cm}^2$
C$48\sqrt{3}\text{cm}^2$
D$64\sqrt{3}\text{cm}^2$

STD 9
Maths
Herons Formula
RD Sharma

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