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# A square and an equilateral triangle have equal sides. If the square

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Math Expert
Joined: 02 Sep 2009
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A square and an equilateral triangle have equal sides. If the square  [#permalink]

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04 Sep 2018, 23:12
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Difficulty:

15% (low)

Question Stats:

88% (00:48) correct 12% (01:27) wrong based on 21 sessions

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A square and an equilateral triangle have equal sides. If the square has diagonal $$10\sqrt{2}$$, what is the area of the triangle?

A. $$50\sqrt{3}$$

B. $$50\sqrt{2}$$

C. 50

D. $$25\sqrt{3}$$

E. 25

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A square and an equilateral triangle have equal sides. If the square  [#permalink]

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04 Sep 2018, 23:26
Attachment:

Diagram.png [ 3.18 KiB | Viewed 353 times ]

Formula used:
Area of equilateral triangle = $$\frac{\sqrt{3}}{4} * a^2$$ where $$a$$ - side of equilateral triangle
Diagonal of square = $$c\sqrt{2}$$ | Area of the square = $$c^2$$ where $$c$$ - side of the square

Given: Diagonal = $$10\sqrt{2}$$. From this we deduce the side of square is 10

One side of the equilateral triangle, which coincides with one of the sides of the triangle, is equal to 10

Therefore, the area of an equilateral triangle is $$\frac{\sqrt{3}}{4} * 10^2 = 25\sqrt{3}$$ (Option D)
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A square and an equilateral triangle have equal sides. If the square  [#permalink]

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05 Sep 2018, 02:52
Bunuel wrote:
A square and an equilateral triangle have equal sides. If the square has diagonal $$10\sqrt{2}$$, what is the area of the triangle?

A. $$50\sqrt{3}$$

B. $$50\sqrt{2}$$

C. 50

D. $$25\sqrt{3}$$

E. 25

The diagonal of a square is given by $$a\sqrt{2}$$

Since diagonal is given to be $$10\sqrt{2}$$,
$$a\sqrt{2}$$ = $$10\sqrt{2}$$,

a = 10

Area of an equilateral triangle is ( $$\sqrt{3}$$ /4)* a^2.
since a = 10,
(( $$\sqrt{3}$$ )/4)* 10^2.
(100/4) * $$\sqrt{3}$$
-> 25$$\sqrt{3}$$

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Re: A square and an equilateral triangle have equal sides. If the square  [#permalink]

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05 Sep 2018, 06:55
Bunuel wrote:
A square and an equilateral triangle have equal sides. If the square has diagonal $$10\sqrt{2}$$, what is the area of the triangle?

A. $$50\sqrt{3}$$

B. $$50\sqrt{2}$$

C. 50

D. $$25\sqrt{3}$$

E. 25

$$a\sqrt{2} = 10\sqrt{2}$$

So, $$a = 10 = s$$

Area of an Equilateral Triangle = $$s^2\sqrt{3}/4$$

Or, Area of an Equilateral Triangle = $$100\sqrt{3}/4$$

Or, Area of an Equilateral Triangle = $$25\sqrt{3}$$, Answer must be (D)
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Re: A square and an equilateral triangle have equal sides. If the square   [#permalink] 05 Sep 2018, 06:55
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