Question

find the length of the third side. if necessary, round to the nearest tenth. 12 14 answer

Explanation:

Step1: Identify the hypotenuse

Since it's a right - triangle, assume the hypotenuse $c$ is the longest side. Here, we need to find the third side. Let the two given sides be $a = 12$ and $b = 14$. We use the Pythagorean theorem $a^{2}+b^{2}=c^{2}$ (if $c$ is the hypotenuse) or $a^{2}+c^{2}=b^{2}$ (if $b$ is the hypotenuse). First, assume $b$ is the hypotenuse.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem for finding a side of a right - triangle is $c=\sqrt{b^{2}-a^{2}}$. Substitute $a = 12$ and $b = 14$ into the formula: $c=\sqrt{14^{2}-12^{2}}=\sqrt{(14 + 12)(14 - 12)}=\sqrt{26\times2}=\sqrt{52}$.

Step3: Calculate the value

$\sqrt{52}=\sqrt{4\times13}=2\sqrt{13}\approx2\times3.606\approx7.2$.

Answer:

$7.2$