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Julian takes a 10-inch by 10-inch square piece of paper and
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06 Oct 2018, 15:22
06 Oct 2018, 15:22
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86% (01:08) correct
13% (01:40) wrong based on 53 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) \(10 +20\sqrt{2}\)
Re: Julian takes a 10-inch by 10-inch square piece of paper and
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13 Apr 2020, 10:36
13 Apr 2020, 10:36
Expert Reply
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
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
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11 May 2020, 06:27
11 May 2020, 06:27
1
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?
The diagonal of the square is 10.root(2) and this forms the base of the triangle obtained when the square is cut in half.
This triangle is cut in half again, giving us a 45-45-90 triangle in which the adjacent side has half the length of the diagonal of the square, namely 5.root(2). The angle opposite to this side is 45 degs. Therefore the other side helping to form the 90 deg also has a length of 5.root(2). The hypotenuse has a given length of 10 inches.
Therefore, the perimeter is 10 + 5.root(2) + 5.root(2) = 10 + 10.root(2). The answer is D.
Alternatively, the sides of a 45-45-90 triangle are in the ratio of x : x: .root(2), where x.root(2) is the hypotenuse.
Since we know the hypotenuse of the 45-45-90 triangle to be 10 inches, the other two sides will be given by [10/root(2)].
Therefore perimeter is 10 + [10/root(2)] + [10/root(2)]
=> 10 + 2.[10/root(2)]
=> 10 + root(2).10
The answer is D.
The diagonal of the square is 10.root(2) and this forms the base of the triangle obtained when the square is cut in half.
This triangle is cut in half again, giving us a 45-45-90 triangle in which the adjacent side has half the length of the diagonal of the square, namely 5.root(2). The angle opposite to this side is 45 degs. Therefore the other side helping to form the 90 deg also has a length of 5.root(2). The hypotenuse has a given length of 10 inches.
Therefore, the perimeter is 10 + 5.root(2) + 5.root(2) = 10 + 10.root(2). The answer is D.
Alternatively, the sides of a 45-45-90 triangle are in the ratio of x : x: .root(2), where x.root(2) is the hypotenuse.
Since we know the hypotenuse of the 45-45-90 triangle to be 10 inches, the other two sides will be given by [10/root(2)].
Therefore perimeter is 10 + [10/root(2)] + [10/root(2)]
=> 10 + 2.[10/root(2)]
=> 10 + root(2).10
The answer is D.
