Question

the area of a rectangle is 105 square units. its width measures 7 units. find the length of its diagonal. round to the nearest tenth of a unit.

Explanation:

Step1: Find the length 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 \( A = 105 \) and \( w = 7 \). So we solve for \( l \):
\( l=\frac{A}{w}=\frac{105}{7} = 15 \)

Step2: Find the length of the diagonal

In a rectangle, the diagonal \( d \) forms a right triangle with the length and width, so we can use the Pythagorean theorem \( d=\sqrt{l^{2}+w^{2}} \). Substituting \( l = 15 \) and \( w = 7 \):
\( d=\sqrt{15^{2}+7^{2}}=\sqrt{225 + 49}=\sqrt{274}\approx16.6 \) (rounded to the nearest tenth)

Answer:

\( 16.6 \)