Question

in $\triangle big$, $bi = 30$, $ig = 50$, and $gb = 40$. which is the hypotenuse of the triangle? $\overline{bi}$ $\overline{ig}$ $\overline{gb}$

Explanation:

Step1: Recall the Pythagorean theorem

In a right - triangle, the hypotenuse is the longest side, and it satisfies the equation $c^{2}=a^{2}+b^{2}$, where $c$ is the hypotenuse and $a,b$ are the other two sides. Also, the hypotenuse is the longest side of the right - triangle.

Step2: Compare the lengths of the sides

We are given that $BI = 30$, $IG=50$ and $GB = 40$.
By comparing the lengths: $30<40<50$, so $BISince the hypotenuse is the longest side in a right - triangle, and among the sides $BI = 30$, $GB = 40$ and $IG = 50$, $IG$ is the longest. So the hypotenuse of $\triangle BIG$ is $\overline{IG}$.

Answer:

$\overline{IG}$