Question

Each leg of a 45 45 90 triangle measures 12cm, what is the length of the hypotenuse

Answer 1

Given that both legs of a 45, 45, and 90 degree triangle are 12cm, find out the length of the hypotenuse.

To solve for the hypotenuse, we will use the Pythagorean Theorem.

The formula to find the hypotenuse is:

a^2 + b^2 = c ^2

We already know that both legs are 12cm, so we can plug them in.

12^2 + 12^2 = c^2

Solve.

144 + 144 = c^2

Add.

288 = c^2

Find the square root of 288.

sqrt(288) = 16.97

Therefore, the square root of 288 is 16.97

If we round 16.97 to 17 and then square it, that would equal 289.

So, the best choice is to leave it as 16.97.

Thus, the length of the hypotenuse is 16.97 or 17 if you want to round it.

Answer 2

12√2

Explanation:

Use the Pythagorean Theorem here:

(12 cm)^2 + (12 cm)^2 = 288 cm^2.

The length of the hypotenuse is √288 = (√4)(√72) = 2(√36)(√2) = 12√2