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# ABC-isoceles right triangle. Perimeter =16+ 16square of 2.

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Manager
Joined: 05 Sep 2007
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ABC-isoceles right triangle. Perimeter =16+ 16square of 2. [#permalink]  28 Oct 2007, 17:04
ABC-isoceles right triangle. Perimeter =16+ 16square of 2. What is the length of the hypotenuse?
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Re: Geometry [#permalink]  28 Oct 2007, 21:13
el1981 wrote:
ABC-isoceles right triangle. Perimeter =16+ 16square of 2. What is the length of the hypotenuse?

I know there is a better way to solve this but I can't remember how to do it.

2x+xsqrt2=16+16sqrt2

x(2+sqrt2)=16+16sqrt2

3.4x=16+16*1.4

3.4x=16+22.4 ---> 3.4x=38.4

x~11.2

11.2 also aprox equals 8sqrt2.

U may be able to do it this way:

(16+16sqrt2)/sqrt2 ---> 16sqrt2/2 +16 ---> 8sqrt2+16. This kinda makes sense.

also note that now 2x +xsqrt2 makes sense. owell sry if i confused u more.
Manager
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Re: Geometry [#permalink]  29 Oct 2007, 05:58
GMATBLACKBELT wrote:
el1981 wrote:
ABC-isoceles right triangle. Perimeter =16+ 16square of 2. What is the length of the hypotenuse?

I know there is a better way to solve this but I can't remember how to do it.

2x+xsqrt2=16+16sqrt2

x(2+sqrt2)=16+16sqrt2

3.4x=16+16*1.4

3.4x=16+22.4 ---> 3.4x=38.4

x~11.2

11.2 also aprox equals 8sqrt2.

U may be able to do it this way:

(16+16sqrt2)/sqrt2 ---> 16sqrt2/2 +16 ---> 8sqrt2+16. This kinda makes sense.

also note that now 2x +xsqrt2 makes sense. owell sry if i confused u more.

So what is the lengh of hypotenuse?
Director
Joined: 11 Jun 2007
Posts: 932
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Re: Geometry [#permalink]  29 Oct 2007, 06:04
el1981 wrote:
GMATBLACKBELT wrote:
el1981 wrote:
ABC-isoceles right triangle. Perimeter =16+ 16square of 2. What is the length of the hypotenuse?

I know there is a better way to solve this but I can't remember how to do it.

2x+xsqrt2=16+16sqrt2

x(2+sqrt2)=16+16sqrt2

3.4x=16+16*1.4

3.4x=16+22.4 ---> 3.4x=38.4

x~11.2

11.2 also aprox equals 8sqrt2.

U may be able to do it this way:

(16+16sqrt2)/sqrt2 ---> 16sqrt2/2 +16 ---> 8sqrt2+16. This kinda makes sense.

also note that now 2x +xsqrt2 makes sense. owell sry if i confused u more.

So what is the lengh of hypotenuse?

hypotenuse = 16
length of other two legs = 8 sqrt 2

check by pythagorean thm: (8 sqrt 2)^2 + (8 sqrt 2)^2 = sqrt(64*2 + 64*2) = sqrt 256 = 16

the perimeter would be 16 + 8 sqrt 2 + 8 sqrt 2 = 16 + 16 sqrt 2 as problem has stated
Re: Geometry   [#permalink] 29 Oct 2007, 06:04
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