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

Question

∆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

GMATinsight · Answer

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

Bunuel · Answer

Copy/paste issue. It's  7√2 , not  72√72 . Edited. Thank you.

Salsanousi · Answer

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

Abhishek009 · Answer

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

ScottTargetTestPrep · Answer

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

HasnainAfxal · Answer

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

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards