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Julian takes a 10-inch by 10-inch square piece of paper and cuts it in

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Julian takes a 10-inch by 10-inch square piece of paper and cuts it in  [#permalink]

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11 Oct 2018, 01:57
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Difficulty:

25% (medium)

Question Stats:

84% (01:51) correct 16% (02:11) wrong based on 45 sessions

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Julian takes a 10-inch by 10-inch square piece of paper and cuts it in half along the diagonal. He then takes one of the halves and cuts it in half again from the corner to the midpoint of the opposite side. All cuts are represented in the figure with dotted lines. What is the perimeter of one of the smallest triangles, in inches?

(A) $$10$$

(B) $$10\sqrt{2}$$

(C) $$20$$

(D) $$10 +10\sqrt{2}$$

(E) $$10 +20\sqrt{2}$$

Attachment:

Capture.JPG [ 14.55 KiB | Viewed 502 times ]

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Julian takes a 10-inch by 10-inch square piece of paper and cuts it in  [#permalink]

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11 Oct 2018, 02:24
Bunuel wrote:

Julian takes a 10-inch by 10-inch square piece of paper and cuts it in half along the diagonal. He then takes one of the halves and cuts it in half again from the corner to the midpoint of the opposite side. All cuts are represented in the figure with dotted lines. What is the perimeter of one of the smallest triangles, in inches?

(A) $$10$$

(B) $$10\sqrt{2}$$

(C) $$20$$

(D) $$10 +10\sqrt{2}$$

(E) $$10 +20\sqrt{2}$$

Attachment:
Capture.JPG

$$c^2 = 10^2 + 10^2 = 200$$

c = $$\sqrt{200}$$ = 10$$\sqrt{2}$$

Half of the hypotenuse is basically the height and base of the triangle .

10$$\sqrt{2}$$/2 = 5$$\sqrt{2}$$.

Perimeter = 5$$\sqrt{2}$$ + 5$$\sqrt{2}$$ + 10 = 2 * 5$$\sqrt{2}$$ + 10

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

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Re: Julian takes a 10-inch by 10-inch square piece of paper and cuts it in  [#permalink]

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11 Oct 2018, 07:40
Bunuel wrote:

Julian takes a 10-inch by 10-inch square piece of paper and cuts it in half along the diagonal. He then takes one of the halves and cuts it in half again from the corner to the midpoint of the opposite side. All cuts are represented in the figure with dotted lines. What is the perimeter of one of the smallest triangles, in inches?

(A) $$10$$

(B) $$10\sqrt{2}$$

(C) $$20$$

(D) $$10 +10\sqrt{2}$$

(E) $$10 +20\sqrt{2}$$

Attachment:
Capture.JPG

Area of a square = Area of 2 Triangles

So, $$10*10 = 2t$$

Or, $$t = 50$$

Diagonal of the Square is $$10\sqrt{2}$$

Now, The small tirangle has sides 1/2 of a Diagonal and the oher side as the side of a square...

So, Perimeter must be $$5\sqrt{2} + 5\sqrt{2} + 10$$ = $$10 +10\sqrt{2}$$ ; Answer must be (D)
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Re: Julian takes a 10-inch by 10-inch square piece of paper and cuts it in  [#permalink]

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11 Oct 2018, 12:20
1
Bunuel wrote:

Julian takes a 10-inch by 10-inch square piece of paper and cuts it in half along the diagonal. He then takes one of the halves and cuts it in half again from the corner to the midpoint of the opposite side. All cuts are represented in the figure with dotted lines. What is the perimeter of one of the smallest triangles, in inches?

(A) $$10$$

(B) $$10\sqrt{2}$$

(C) $$20$$

(D) $$10 +10\sqrt{2}$$

(E) $$10 +20\sqrt{2}$$

Attachment:
Capture.JPG

Diameter of a square S√2= 10√2
Since we have to take half of the diameter for 2 of the triangle side we have 10√2/2= 5√2
perimeter - 5√2+5√2+10 or 10+10√2
Re: Julian takes a 10-inch by 10-inch square piece of paper and cuts it in   [#permalink] 11 Oct 2018, 12:20
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