Question

the area of a rectangle is 135 square units. its length measures 9 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 \( A = 135 \) and \( l = 9 \), so we can solve for \( w \):

$$ w=\frac{A}{l}=\frac{135}{9} = 15 $$

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 \( l = 9 \) and \( w = 15 \):

$$ d=\sqrt{9^{2}+15^{2}}=\sqrt{81 + 225}=\sqrt{306}\approx17.5 $$

Answer:

The length of the diagonal is approximately \(\boxed{17.5}\) units.