Question

a rectangle has a width of 9 units and a length of 40 units. what is the length of a diagonal?
31 units
39 units
41 units
49 units

Explanation:

Step1: Apply Pythagorean theorem

In a rectangle, if the length is $l = 40$, the width is $w=9$, and the diagonal is $d$, by the Pythagorean theorem $d^{2}=l^{2}+w^{2}$.

Step2: Calculate $l^{2}+w^{2}$

$l^{2}=40^{2}=1600$, $w^{2}=9^{2}=81$. Then $l^{2}+w^{2}=1600 + 81=1681$.

Step3: Find the diagonal length

$d=\sqrt{1681}=41$.

Answer:

C. 41 units