Question

use the pythagorean theorem quick check
if a right triangle has legs that are both 12 cm long, how long is the hypotenuse? round the answer to the nearest hundredth. (1 point)
16.97
not enough information is given to solve the problem.
288
170

Explanation:

Step1: Recall Pythagorean Theorem

The Pythagorean Theorem for a right triangle is \(a^{2}+b^{2}=c^{2}\), where \(a\) and \(b\) are the legs, and \(c\) is the hypotenuse. Here, \(a = b=12\) cm.

Step2: Substitute values into the formula

Substitute \(a = 12\) and \(b = 12\) into the formula: \(12^{2}+12^{2}=c^{2}\). Calculate \(12^{2}=144\), so \(144 + 144=c^{2}\), which simplifies to \(288=c^{2}\).

Step3: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{288}\). Simplify \(\sqrt{288}=\sqrt{144\times2}=12\sqrt{2}\approx16.97\) (rounded to the nearest hundredth).

Answer:

16.97