Geomatry questions

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alltimeacheiver: Master | Next Rank: 500 Posts; Posts: 183; Joined: Wed Feb 09, 2011 3:08 amFollowed by: 5 members; Location: Delhi; Thanked: 1 times

by alltimeacheiver » Fri Feb 18, 2011 3:08 am

HI Gmat Guns,

I hope this posting is clear. I got and e but the right ans is b. source gmat Prep questiion bank

Perimeter of isosceles right triangle is 16 +16âˆš2, what is hypotenuse?
a. 8
b. 16
c. 4âˆš2
d. 8âˆš2
e. 16âˆš2

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Source: Beat The GMAT — Problem Solving | Fri Feb 18, 2011 3:08 am

sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Fri Feb 18, 2011 3:19 am

alltimeacheiver wrote:HI Gmat Guns,

I hope this posting is clear. I got and e but the right ans is b. source gmat Prep questiion bank

Perimeter of isosceles right triangle is 16 +16âˆš2, what is hypotenuse?
a. 8
b. 16
c. 4âˆš2
d. 8âˆš2
e. 16âˆš2

The perimeter of an isosceles right triangle, with its hypotenues as x, is always in the form x + x sqrt 2. So if perimeter is 16 + 16 sqrt 2, hypotenues is 16.

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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alltimeacheiver: Master | Next Rank: 500 Posts; Posts: 183; Joined: Wed Feb 09, 2011 3:08 amFollowed by: 5 members; Location: Delhi; Thanked: 1 times

by alltimeacheiver » Fri Feb 18, 2011 3:43 am

Isoceles triangle has property that 2 sides are equal. so I thought 16 Squart 2 is hypotenuse becoz of x, x, x suart 2 ie 45, 45, 90. can u tell where i was wrong...

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Fri Feb 18, 2011 3:57 am

The perimeter of a certain isosceles right triangle is 16 + 16âˆš2. What is the length of the hypoteneuse?
a. 8
b. 16
c. 4âˆš2
d. 8âˆš2
e. 16âˆš2

OA is b.
Could someone please explain this answer?
thanks

The sides of an isosceles right triangle are proportioned: s - s - sâˆš2.
So if s=side and h=hypotenuse, then h = sâˆš2 and s = h/âˆš2.

We can plug in the answers, which represent the hypotenuse.

Answer choice C: h = 4âˆš2
s = (4âˆš2)/âˆš2 = 4.
p = 4 + 4 + 4âˆš2 = 8 + 4âˆš2.
Eliminate C. The perimeter needs to be quite a bit larger.

Answer choice B: h = 16
s = 16/âˆš2 = (16*âˆš2)/(âˆš2*âˆš2) = (16âˆš2)/2 = 8âˆš2.
p = 8âˆš2 + 8âˆš2 + 16 = 16 + 16âˆš2. Success!

The correct answer is B.

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alltimeacheiver: Master | Next Rank: 500 Posts; Posts: 183; Joined: Wed Feb 09, 2011 3:08 amFollowed by: 5 members; Location: Delhi; Thanked: 1 times

by alltimeacheiver » Fri Feb 18, 2011 4:04 am

Thankssssssssssss sir I got now.

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Fri Feb 18, 2011 4:06 am

alltimeacheiver wrote:Isoceles triangle has property that 2 sides are equal. so I thought 16 Squart 2 is hypotenuse becoz of x, x, x suart 2 ie 45, 45, 90. can u tell where i was wrong...

If you take x as a leg of the isosceles triangle, then x âˆš2 is its diagonal, and consequently the perimeter is

x + x + x âˆš2 = 2 x + x âˆš2 = 16 +16âˆš2 (given)

or 2 x - 16 = âˆš2 (16 - x), squaring you get

4 x^2 - 64 x + 256 = 512 - 64 x + 2 x^2

or 2 x^2 = 256

or x = 16/âˆš2

or the diagonal x âˆš2 = 16

But it includes tedious calculations, so just rely on the fact that the perimeter of an isosceles right triangle, with its hypotenuse as x, is always in the form x + x âˆš2, and save time on test.

If hypotenuse is x, then each leg is x/âˆš2, and perimeter is x + x/âˆš2 + x/âˆš2 = x + x âˆš2, simple to compare now!

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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