Question

what is the formula to calculate the diagonal of a rectangle with length ( l ) and width ( w )?
a. ( sqrt{l^{2}+w^{2}} )
b. ( l^{2}-w^{2} )
c. ( l + w )
d. ( l^{2}+w^{2} )

Explanation:

Step1: Consider the rectangle and its diagonal

A rectangle's diagonal forms a right - triangle with the length and width.

Step2: Apply the Pythagorean theorem

In a right - triangle with sides \(a = l\), \(b = w\) and hypotenuse \(c\) (the diagonal), by the Pythagorean theorem \(c^{2}=a^{2}+b^{2}\). So \(c=\sqrt{l^{2}+w^{2}}\).

Answer:

A. $\sqrt{l^{2}+w^{2}}$