Question

a mouse has made holes in opposite corners of a rectangular kitchen. the kitchen is 3 meters by 4 meters. if the mouse runs straight from one hole to the other, how far will it run? meters

Explanation:

Step1: Identify right - triangle sides

The length and width of the rectangle form the two legs of a right - triangle. Let $a = 3$ meters and $b = 4$ meters.

Step2: Apply Pythagorean theorem

The Pythagorean theorem is $c^{2}=a^{2}+b^{2}$, where $c$ is the length of the hypotenuse. Substitute $a = 3$ and $b = 4$ into the formula: $c^{2}=3^{2}+4^{2}=9 + 16=25$.

Step3: Solve for $c$

Take the square root of both sides. Since $c>0$, $c=\sqrt{25}=5$.

Answer:

5