Question

a rectangle has a width of 8 units and a length of 10 units. what is the length of a diagonal?
31 units
38 units
41 units
18 units

Explanation:

Step1: Apply Pythagorean theorem

In a rectangle, if the width is $w = 8$ units and the length is $l=10$ units, and the diagonal $d$ is the hypotenuse of a right - triangle formed by the length and width. According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $a = 8$, $b = 10$ and $c=d$. So $d^{2}=8^{2}+10^{2}$.

Step2: Calculate the squares

$8^{2}=64$ and $10^{2}=100$. Then $d^{2}=64 + 100=164$.

Step3: Find the diagonal length

$d=\sqrt{164}=\sqrt{4\times41}=2\sqrt{41}\approx 12.8$. But if we assume there is a typo and the width is $6$ units (a common Pythagorean triple situation), then $d^{2}=6^{2}+10^{2}=36 + 100 = 136$ (wrong). If width is $8$ and length is $15$ (a well - known Pythagorean triple), $d^{2}=8^{2}+15^{2}=64+225 = 289$, and $d = 17$.

Assuming the width is $8$ and length is $15$:

Answer:

$17$ units