Question

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.
answer attempt 1 out of 2

Explanation:

Step1: Find the width of the rectangle

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

Step2: Calculate the diagonal using the Pythagorean theorem

For a rectangle, the diagonal \( d \) forms a right triangle with length \( l \) and width \( w \). The Pythagorean theorem states \( d=\sqrt{l^{2}+w^{2}} \). Substituting \( l = 20 \) and \( w = 19 \):
\( d=\sqrt{20^{2}+19^{2}}=\sqrt{400 + 361}=\sqrt{761}\approx27.6 \) (rounded to the nearest tenth)

Answer:

\( 27.6 \)