The area of a rectangle is 342 square units. Its length measures 19 units. Find the length of its diagonal. Round to the nearest tenth of a unit.

Question

asked Feb 18, 2022 214k views

1 Answer

Shrinivas · Answer 1 · 2022-02-23T21:27:06+0000

Answer:

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

Step-by-step explanation:

From Geometry we remember that the area of the rectangle (
), in square units, is described by this formula:

$A = w\cdot l$ (1)

Where:

- Width, in units.

- Length, in units.

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

w = (A)/(l)

$w = (342\,u^(2))/(19\,u)$

$w = 18\,u$

And the length of the diagonal (
), 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.