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∆ABC is a right-angled isosceles triangle, and ∠B is the right angle

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

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New post Updated on: 15 Jul 2019, 04:18
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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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New post Updated on: 09 Oct 2018, 04:24
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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. \(Side, a = 7 =AB = BC\)

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

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New post 09 Oct 2018, 04:21
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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New post 09 Oct 2018, 05:04
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

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

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New post 09 Oct 2018, 08:21
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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New post 12 Oct 2018, 07:52
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.

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

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New post 13 Oct 2018, 01:53
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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Re: ∆ABC is a right-angled isosceles triangle, and ∠B is the right angle   [#permalink] 13 Oct 2018, 01:53
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