Question

The area of a rectangle is 342 square units. Its length measures 19 units. Find the

Answer 1

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 ($A$), in square units, is described by this formula:

$A = w\cdot l$ (1)

Where:

$w$ - Width, in units.

$l$ - Length, in units.

If we know that $A = 342\,u^{2}$ and $l = 19\,u$, then the width of the rectangle is:

$w = \frac{A}{l}$

$w = \frac{342\,u^{2}}{19\,u}$

$w = 18\,u$

And the length of the diagonal ($d$), in units, is determined by the Pythagorean Theorem:

$d = \sqrt{w^{2}+l^{2}}$ (2)

If we know that $w = 18\,u$ and $l = 19\,u$, then the length of the diagonal is:

$d = \sqrt{(18\,u)^{2} + (19\,u)^{2}}$

$d \approx 26.2\,u$

The length of the diagonal of the rectangle is approximately 26.2 units.