Question

wesley takes a piece of plywood that is 12 inches long and uses a table saw to make a 20 - inch cut from corner to opposite corner. what was the width of the piece of plywood? inches

Explanation:

Step1: Apply Pythagorean theorem

The length ($l = 12$ inches), width ($w$) and diagonal ($d=20$ inches) of the plywood form a right - triangle. By the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse (diagonal) and $a$ and $b$ are the other two sides (length and width). So, $l^{2}+w^{2}=d^{2}$.

Step2: Rearrange the formula to solve for width

We can rewrite the formula as $w^{2}=d^{2}-l^{2}$. Substitute $l = 12$ and $d = 20$ into the formula: $w^{2}=20^{2}-12^{2}$.

Step3: Calculate the values

First, calculate $20^{2}=400$ and $12^{2}=144$. Then $w^{2}=400 - 144=256$.

Step4: Find the width

Take the square root of both sides. Since width cannot be negative, $w=\sqrt{256}=16$.

Answer:

16