Question

colleen takes a rectangular piece of fabric and cuts from one corner to the opposite corner. the piece of fabric is 8.4 inches long and 3.4 inches wide, how long is the diagonal cut that colleen made? if necessary, round to the nearest tenth. inches

Explanation:

Step1: Apply Pythagorean theorem

For a rectangle with length $l = 8.4$ inches and width $w=3.4$ inches, the diagonal $d$ satisfies $d^{2}=l^{2}+w^{2}$. So $d=\sqrt{l^{2}+w^{2}}=\sqrt{8.4^{2}+3.4^{2}}$.

Step2: Calculate squares

$8.4^{2}=8.4\times8.4 = 70.56$ and $3.4^{2}=3.4\times3.4 = 11.56$. Then $l^{2}+w^{2}=70.56 + 11.56=82.12$.

Step3: Find square - root

$d=\sqrt{82.12}\approx9.1$ inches.

Answer:

$9.1$ inches