Geomatry questions

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 +16√2, what is hypotenuse?
a. 8
b. 16
c. 4√2
d. 8√2
e. 16√2

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.

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...

The perimeter of a certain isosceles right triangle is 16 + 16√2. What is the length of the hypoteneuse?
a. 8
b. 16
c. 4√2
d. 8√2
e. 16√2

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

The sides of an isosceles right triangle are proportioned: s - s - s√2.
So if s=side and h=hypotenuse, then h = s√2 and s = h/√2.

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

Answer choice C: h = 4√2
s = (4√2)/√2 = 4.
p = 4 + 4 + 4√2 = 8 + 4√2.
Eliminate C. The perimeter needs to be quite a bit larger.

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

The correct answer is B.

Thankssssssssssss sir I got now.

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 √2 is its diagonal, and consequently the perimeter is

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

or 2 x – 16 = √2 (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/√2

or the diagonal x √2 = 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 √2, and save time on test.

If hypotenuse is x, then each leg is x/√2, and perimeter is x + x/√2 + x/√2 = x + x √2, simple to compare now!