Question

the area of a rectangle is 380 square units. its length measures 20 units. find the length of its diagonal. round to the nearest tenth of a unit.

Explanation:

Step1: Find the width of the rectangle

The area of a rectangle is given by the formula \( A = l \times w \), where \( A \) is the area, \( l \) is the length, and \( w \) is the width. We know \( A = 380 \) and \( l = 20 \), so we can solve for \( w \):
\( w=\frac{A}{l}=\frac{380}{20} = 19 \)

Step2: Use the Pythagorean theorem to find the diagonal

In a rectangle, the diagonal \( d \) forms a right triangle with the length and width, so by the Pythagorean theorem \( d=\sqrt{l^{2}+w^{2}} \). Substituting \( l = 20 \) and \( w = 19 \):
\( d=\sqrt{20^{2}+19^{2}}=\sqrt{400 + 361}=\sqrt{761}\approx27.6 \)

Answer:

\( 27.6 \)