The length of the hypotenuse of a 45°-45°-90° triangle is 16 cm. What is the length of each leg?

Answer 1

Because this is 45-45-90 triangle, the two sides (other than the hypotenuse) must be equal. Let x = that length. Now, apply the Pythagorean theorem (a² + b² = c²). In this problem, a = b = x and c = 16 cm. So,

x² + x² = 16² cm²

Or, 2x² = 16² cm² and x² = 16²/2 cm²

Taking the square root of both sides gives x = 16 / (2^1/2) cm, which means that the length of each leg is approximately equal to 11.31 cm.

Answer 2

The relationship of a 45-45-90 triangle sides is 1-1-√2.

If you set up a proportion

1/√2 =x/16 Cross multiply

√2x=16 Divide both sides by √2

√2x/√2=16/√2 Simplify

x=16/√2

If you rationalize it:

(16/√2)(√2/√2)

16/2√2

8√2

Answer 3

a^2 + b^2 = c^2 pythagorean theorem

The two legs are the same length, since it's a 45-45-90 triangle, so we can say, 2a^2 = c^2

Rewrite:

2a^2 = 16^2

2a^2 = 256

a^2 = 128

square root of each side = a = square root of 128

128 is the same as 64/2, 64 has a perfect square root of 8, making the final answer a = 8(square root of 2)

You can plug that answer into the original equation and you will balance it:

(8(square root 2))^2 + (8(square root 2))^2 = 256