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Math Expert V
Joined: 02 Sep 2009
Posts: 58335
∆ABC is a right-angled isosceles triangle, and ∠B is the right angle  [#permalink]

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Difficulty:   5% (low)

Question Stats: 98% (00:59) correct 2% (01:18) wrong based on 42 sessions

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∆ABC is a right-angled isosceles triangle, and ∠B is the right angle in the triangle. If AC measures $$7√2$$, then which one of the following would equal the lengths of AB and BC, respectively?

(A) 7, 7
(B) 9, 9
(C) 10, 10
(D) 11, 12
(E) 7, 12

Source: Nova GMAT
Difficulty Level: 500

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Originally posted by Bunuel on 09 Oct 2018, 01:37.
Last edited by SajjadAhmad on 15 Jul 2019, 04:18, edited 1 time in total.
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Re: ∆ABC is a right-angled isosceles triangle, and ∠B is the right angle  [#permalink]

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Bunuel wrote:
∆ABC is a right-angled isosceles triangle, and ∠B is the right angle in the triangle. If AC measures 72√72 , then which one of the following would equal the lengths of AB and BC, respectively?

(A) 7, 7
(B) 9, 9
(C) 10, 10
(D) 11, 12
(E) 7, 12

$$AC = Hypotenuse = a√2 = 7√2$$ where $$a$$ is the side of the triangle i.e. $$AB = BC = a$$

i.e. $$Side, a = 7 =AB = BC$$

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Originally posted by GMATinsight on 09 Oct 2018, 04:16.
Last edited by GMATinsight on 09 Oct 2018, 04:24, edited 1 time in total.
Math Expert V
Joined: 02 Sep 2009
Posts: 58335
Re: ∆ABC is a right-angled isosceles triangle, and ∠B is the right angle  [#permalink]

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GMATinsight wrote:
Bunuel wrote:
∆ABC is a right-angled isosceles triangle, and ∠B is the right angle in the triangle. If AC measures 72√72 , then which one of the following would equal the lengths of AB and BC, respectively?

(A) 7, 7
(B) 9, 9
(C) 10, 10
(D) 11, 12
(E) 7, 12

$$AC = Hypotenuse = a√2 = 72√72$$

i.e. $$Side, a = 72*6 = 432$$

Bunuel As per the given information my answer seems correct but I am sure there is a little type error here. Copy/paste issue. It's $$7√2$$, not $$72√72$$. Edited. Thank you.
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Re: ∆ABC is a right-angled isosceles triangle, and ∠B is the right angle  [#permalink]

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Bunuel wrote:
∆ABC is a right-angled isosceles triangle, and ∠B is the right angle in the triangle. If AC measures $$7√2$$, then which one of the following would equal the lengths of AB and BC, respectively?

(A) 7, 7
(B) 9, 9
(C) 10, 10
(D) 11, 12
(E) 7, 12

A right angled isosceles would be 45:45:90

45:45:90 would be x:x:x$$\sqrt{2}$$

x$$\sqrt{2}$$ = 7$$\sqrt{2}$$
making x be 7

so it would be 7,7

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Re: ∆ABC is a right-angled isosceles triangle, and ∠B is the right angle  [#permalink]

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Bunuel wrote:
∆ABC is a right-angled isosceles triangle, and ∠B is the right angle in the triangle. If AC measures $$7√2$$, then which one of the following would equal the lengths of AB and BC, respectively?

(A) 7, 7
(B) 9, 9
(C) 10, 10
(D) 11, 12
(E) 7, 12

The Triangle is Right angled at B = AC is the Hypotenuse = $$7√2$$

The hypotenuse of a Right isosceles triangle is $$a√2$$ = $$7√2$$

Thus, $$a = 7$$, Answer must be (A) 7,7
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Re: ∆ABC is a right-angled isosceles triangle, and ∠B is the right angle  [#permalink]

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Bunuel wrote:
∆ABC is a right-angled isosceles triangle, and ∠B is the right angle in the triangle. If AC measures $$7√2$$, then which one of the following would equal the lengths of AB and BC, respectively?

(A) 7, 7
(B) 9, 9
(C) 10, 10
(D) 11, 12
(E) 7, 12

A 45-45-90 right triangle has side ratios of x : x : x√2,where x√2 is the length of the hypotenuse. We see that triangle ABC can have sides of 7, 7, and 7√2.

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Re: ∆ABC is a right-angled isosceles triangle, and ∠B is the right angle  [#permalink]

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according to given information its a $$90-45-45$$ triangle with 90 at B.
length of opposite side to 90 degree is given $$(7\sqrt{2})$$
as lengths of sides in $$90-45-45$$ triangle are $$\sqrt{2}x,x,x$$
So side lengths of other two sides are $$7\sqrt{2}/\sqrt{2}=7$$
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Hitting Kudos is the best way of appreciation. Eric Thomas, "When you want to succeed as bad as you want to breathe, then you'll be successful." Re: ∆ABC is a right-angled isosceles triangle, and ∠B is the right angle   [#permalink] 13 Oct 2018, 01:53
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