Math Pythagorean theorem help

Question

The hypotenuse of a right triangle is twice ass long as one of the legs. If the perimeter of the triangle is 25 cm, determine the length of the hypotenuse, accurate to three places after the decimal point.

Answer 1

Let a and b be the legs of the right triangle, and c - its hypotenuse. Then

a² + b² = c²

Because the hypotenuse is twice as long as one of the legs, we can write

c = 2a

Perimeter p = a + b + c

Or p = a + b + 2a

p = 3a + b (1)

Now the Pythagorean theorem could be written as

a² + b² = 4a²

Or b² = 3a²

Hence b .= a√3

Now let's put this value in equation for perimeter of the triangle (1)

We have

p = 3a + a√3

After factoring

p = a(3 + √3)

Now we will use the fact that p = 25 cm.

a(3 + √3) = 25,

then

a = 25 / (3 + √3)

But c = 2a, so finally

c = 50 /(3 + √3)

Putting numeric values, we obtain

c = 50 / (3 + 1.732) = 10.566

Answer: 10.566 cm

P.S. From the standpoint of theory of measurements and errors, to give 3 decimal places does not make any sense in this problem, because the perimeter is a whole number (no decimal places at all).

It would make any sense only, if the perimeter p = 25.000 cm!