Answer :
Answer:
The length of the diagonal of the rectangle is approximately 26.2 units.
Explanation:
From Geometry we remember that the area of the rectangle ([tex]A[/tex]), in square units, is described by this formula:
[tex]A = w\cdot l[/tex] (1)
Where:
[tex]w[/tex] - Width, in units.
[tex]l[/tex] - Length, in units.
If we know that [tex]A = 342\,u^{2}[/tex] and [tex]l = 19\,u[/tex], then the width of the rectangle is:
[tex]w = \frac{A}{l}[/tex]
[tex]w = \frac{342\,u^{2}}{19\,u}[/tex]
[tex]w = 18\,u[/tex]
And the length of the diagonal ([tex]d[/tex]), in units, is determined by the Pythagorean Theorem:
[tex]d = \sqrt{w^{2}+l^{2}}[/tex] (2)
If we know that [tex]w = 18\,u[/tex] and [tex]l = 19\,u[/tex], then the length of the diagonal is:
[tex]d = \sqrt{(18\,u)^{2} + (19\,u)^{2}}[/tex]
[tex]d \approx 26.2\,u[/tex]
The length of the diagonal of the rectangle is approximately 26.2 units.