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# Will someone please help me...I thought U and V equaled 4 times the square root of 2. But according to my answer sheet it’s 4. Help!?

### 9 Answers

- TomVLv 76 months agoFavorite Answer
It's an isosceles triangle so u and v are equal and Pythagoras requires that

u² + v² = (8√2)²

Since u = v then u² + v² = 2u² = 2v² = 128

2u² = 2v² = 128

u² = v² = 64

u = v = 8

If the answer sheet says u = v = 4, then the answer sheet is wrong.

- 6 months ago
This is a 45°-45°-90° triangle so that u = v.

By Pythagorean Theorem,

u²+v² = (8√2)² = [√(8² * 2)]² = [√(64*2)]² = [√128]² = 128

2u² = 128

u² = 64 or u = v = √64 = 8

For this special isosceles right triangle, remembering the corresponding sides have the ratio,

u:v:hypotenuse = 1:1:√2 from geometry, it would have been easier to find u or v by dividing 8√2 by √2.

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- Ian HLv 76 months ago
u^2 + v^2 = 64 *2

u = v, so u^2 + v^2 = 2u^2 = 64 *2

u = 8 = v

We all agree that the answer sheet was wrong for once.

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- PinkgreenLv 76 months ago
By the Pythagorean, sqr(u^2+v^2)=8sqr(2)

=>

sqr(2u^2)=8sqr(2)...[ u=v ]

=>

sqr(2)u=8sqr(2)

=>

u=8....[cancelling the sqr(2)]

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- DavidLv 76 months ago
It is an isosceles right angle triangle and the values of u and v works out as 8

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- ?Lv 76 months ago
// Your answer sheet is incorrect.

The sides of a 45-45-90 triangles have a special ratio to each other:

..........leg1 : leg2 : hypotenuse

............1....:..1....:.......√2

In this problem, the hypotenuse is 8√2. That means that u and v are

....................................8√2

.................................-------- = 8.................ANS

....................................√2

..........leg1 : leg2 : hypotenuse

............1....:..1....:.......√2

..........u=8..:..v=8.:....8√2

Thank you so much!

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- D gLv 76 months ago
u ^2 +V^2 =8sqrt(2)

sin 45 = o / h = u / 8sqrt(2) = 1 / sqrt(2)

u = 8sqrt(2)/ sqrt(2)

u = 8

and v = 8

because its 45 degs

if you squre the hypoteneuse you get 64x2 which is the sum of 8^2 and 8^2

- ...Show all comments
Huh? You should start with u^2 + v^2 = (8√2)^2.

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- Some BodyLv 76 months ago
In a 45-45-90 triangle, the two short sides are the same length and the hypotenuse is the length of the short side times √2.

Here, the hypotenuse is 8√2, so u = v = 8.

- ...Show all comments
Thanks! So helpful

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Thank you so much. You really helped me with this problem that I was stuck on.