Question

the picture frame below is a rectangle with dimensions 10 inches by 8 inches. what is the length of the diagonal of the picture frame? round your answer to the nearest tenth if necessary. a. 10.4 inches b. 12.8 inches c. 8.6 inches d. 6 inches

Explanation:

Step1: Apply Pythagorean theorem

In a rectangle, if the length is $l = 10$ inches and the width is $w = 8$ inches, and the diagonal is $d$. According to the Pythagorean theorem $d^{2}=l^{2}+w^{2}$. So $d^{2}=10^{2}+8^{2}$.

Step2: Calculate the sum of squares

$10^{2}=100$ and $8^{2}=64$, then $10^{2}+8^{2}=100 + 64=164$. So $d^{2}=164$.

Step3: Find the value of the diagonal

$d=\sqrt{164}\approx 12.8$ inches.

Answer:

B. 12.8 inches