if the square root of "a" squared + "b" squared = 56, what would "a" and "b" be if they are the same length?

Question

sqrt of (a^2 + b^2) = 56

the hypotenuse (sp?) of a right angle is 56. What are the lengths of the sides?

Answer 1

√(a^2+b^2)=√(2a^2) when a =b
√(2a^2)=56
2a^2 = 56*56
a^2= 28*56
= 4*7*4*7*2
a= 4*7√2
= 28√2
but a=b
so a=b=28√2

Answer 2

Do me a favor and rewrite the equation for the problem. I'm not sure if you mean...
1. rt (a^2 + b^2) = 56
or
2. rt(a^2) + b^2 = 56

These two would lead to very different answers.

Thanks for the additional information.

So if a^2 + b^2 = 56^2

a^2 + a^2 = 3136 (replace b with a)

2a^2 = 3136

Divide by 2.
a^2 = 1568

Square root both sides
a = rt784 * rt2 (784*2 = 1568)

a = 28rt2 (square root of 784 = 28

So a = b = 28 rt2.

Hope this helps. Good Luck. :)

Answer 3

given sqrt(a^2+b^2)=56.

square both sides, you get
a^2+b^2=56^2

if a= b, then substitute, b=a.

therefore, you can rewrite the equation as
2a ^ 2=56 ^ 2
ie, a^2=56 x 28

or a^2=1568

therefore a= sqrt(1568)=39.59..

since a and b are same length,
a = b = 39.59 at the second decimal place.

Answer 4

seems to work out to

a + b^2 = 56
since a = b,

a + a^2 = 56

a^2 + a - 56 = 0

(a-8)(a+7) = 0

So a = 8 or a = -7 (rejected since a is a length)

so therefore a = 8 and b = 8

Answer 5

square root cancels out the 2 squared
this leaves

a + b = 56

so if a and b is the same length

56/2 = 28

a=28 b=28

Answer 6

a=b=28

Answer 7

sqrt [a^2 + b^2] = 56

squaring both sides we get,

a^2 + b^2 = 3136

since, a = b

therefore,

2a^2 = 3136

a^2 = 1568

a = 39.6

The lengths are 39.6 units each.

Answer 8

sqrt 28 or 2xsqrt7