Question

(c) Express the diagonal of a rectangle, D, in terms of its width, w, if the area of the rectangle is 13 square feet.

D(w) =

Answer 1

Diagonal of a rectangle:
D²=W²+L² ( W-width, L-length)
The area : W*L= 13 ⇒ L=
`(13)/(W)`
D=
`\sqrt{W^(2) + ((13)/(W))^(2) } = \sqrt{W^(2) + (169)/(W^(2) ) }= \\ = \sqrt{ (W^(4)+169 )/(W^(2) ) }= \frac{ \sqrt{W^(4) +169} }{W}`