Question

baked pita chips are often in the shape of 45 - 45 - 90 triangles. caitlyn determines that the longest side of a pita chip in one bag measures 3 centimeters. what is the length of the other sides of the pita chips? centimeters what is the area of the pita chip? square centimeters

Explanation:

Step1: Identify the type of triangle

The pita - chip is in the shape of a 45 - 45 - 90 triangle. In a 45 - 45 - 90 triangle, the ratio of the sides is $1:1:\sqrt{2}$. Given one side is 3 centimeters. Since the two legs (shorter sides) of a 45 - 45 - 90 triangle are equal, the other non - hypotenuse side is also 3 centimeters.

Step2: Calculate the length of the hypotenuse

The formula for the hypotenuse $c$ of a 45 - 45 - 90 triangle with leg length $a$ is $c = a\sqrt{2}$. Here $a = 3$ cm, so the hypotenuse $c=3\sqrt{2}$ cm.

Step3: Calculate the area of the triangle

The area formula for a triangle is $A=\frac{1}{2}bh$. In a 45 - 45 - 90 triangle, if the base $b$ and height $h$ are the legs of the triangle, and $b = h=3$ cm, then $A=\frac{1}{2}\times3\times3=\frac{9}{2}=4.5$ square centimeters.

Answer:

The length of the other non - hypotenuse side is 3 centimeters and the area of the pita chip is 4.5 square centimeters.