Isosceles Right Triangle

[heshamelaziry]

The perimeter of a certain Isosceles right triangle is 16 + 16√2. What is the length of the hypotenuse of the triangle ?

[xcusemeplz2009]

h is 16

h^2=2*a^2=>h=asqrt(2)

2a+h=16+16sqrt(2)

2a+sqrt(2)=16+16sqrt(2)

solving a=8*sqrt(2)
h=8*sqrt2*sqrt2=16

[NikolayZ]

Hey there !

Since you have an isosceles triangle, its perimeter = 2x+y. ( 2 sides are x, and the hypotenuse is y)
so the perimeter is
16+16sqrt(2)=2x+y.
Also the hypotenuse equals xsqrt(2), since it is 45 degree isosceles right triangle.

16+16sqrt(2)=2x+xsqrt(2)

x= (16+16*sqrt(2)/(2+sqrt(2))
Then , hypotenuse will be x*sqrt(2)= (16*sqrt(2)+32)/(sqrt(2)+2)=16.

[heshamelaziry]

Hey there !

Since you have an isosceles triangle, its perimeter = 2x+y. ( 2 sides are x, and the hypotenuse is y)
so the perimeter is
16+16sqrt(2)=2x+y.
Also the hypotenuse equals xsqrt(2), since it is 45 degree isosceles right triangle.

16+16sqrt(2)=2x+xsqrt(2)

x= (16+16*sqrt(2)/(2+2*sqrt(2))
Then , hypotenuse will be x*sqrt(2)= (16*sqrt(2)+32)/(sqrt(2)+2)=16.

[NikolayZ]

Sorry mate. "typo happens" (c) =) corrected.

[heshamelaziry]

Sorry mate. "typo happens" (c) =) corrected.

I got it, finally. Thanks a lot.

[NikolayZ]

heshamelaziry, truly there is a flaw in my solvent, because it is not consistent =(

so, right answer to my mind is

2x+x*sqrt(2)=16+16*sqrt(2)
x(2+sqrt(2)=16+16*sqrt(2)
x=(16+16*sqrt(2))/2+sqrt(2)
x*sqrt(2)=(16*sqrt(2)+16*sqrt(2)*sqrt(2))/2+sqrt(2)
==> since hte x*sqrt(2) is the hypotenuse (h)
then
h=(16*sqrt(2)+32)/2+sqrt(2)
factorizing 16 from the numerator we'll get
16(sqrt(2)+2)/(sqrt(2)+2)=16.

[heshamelaziry]

heshamelaziry, truly there is a flaw in my solvent, because it is not consistent =(

so, right answer to my mind is

2x+x*sqrt(2)=16+16*sqrt(2)
x(2+sqrt(2)=16+16*sqrt(2)
x=(16+16*sqrt(2))/2+sqrt(2)
x*sqrt(2)=(16*sqrt(2)+16*sqrt(2)*sqrt(2))/2+sqrt(2)
==> since hte x*sqrt(2) is the hypotenuse (h)
then
h=(16*sqrt(2)+32)/2+sqrt(2)
factorizing 16 from the numerator we'll get
16(sqrt(2)+2)/(sqrt(2)+2)=16.

Thanks Dude I posted some problems form a GMATPrep test that I took. Maybe you like to take a shot at them. I posted them yesterday in an attachement.

[kkpatel1]

heshamelaziry, truly there is a flaw in my solvent, because it is not consistent =(

so, right answer to my mind is

2x+x*sqrt(2)=16+16*sqrt(2)
x(2+sqrt(2)=16+16*sqrt(2)
x=(16+16*sqrt(2))/2+sqrt(2)
x*sqrt(2)=(16*sqrt(2)+16*sqrt(2)*sqrt(2))/2+sqrt(2)
==> since hte x*sqrt(2) is the hypotenuse (h)
then
h=(16*sqrt(2)+32)/2+sqrt(2)
factorizing 16 from the numerator we'll get
16(sqrt(2)+2)/(sqrt(2)+2)=16.

Where I am confused is:
When you set:
x*sqrt(2)=[(16*sqrt(2)+16*sqrt(2)*sqrt(2)]/2+sqrt(2)

why dont you multiply the bottom portion by sqrt(2) also, since the rule is, if you multiply one thing by something, you have to do it to everything!??

therefore shouldnt it be: h=(16*sqrt(2)+32)/2+2 ??