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.

Steps to Solve

1. Calculate the length of the rectangle

We know that the area of a rectangle is given by the formula $Area = length \times width$. We are given the area (105 square units) and the width (7 units). We can solve for the length.

$105 = length \times 7$

$length = \frac{105}{7} = 15$ units

2. Use the Pythagorean theorem to find the diagonal

The diagonal of a rectangle forms a right triangle with the length and width as its legs. We can use the Pythagorean theorem to find the length of the diagonal, $d$. The Pythagorean theorem states that $a^2 + b^2 = c^2$, where $a$ and $b$ are the lengths of the legs of a right triangle, and $c$ is the length of the hypotenuse. In this case, the length and width of the rectangle are the legs, and the diagonal is the hypotenuse.

$d^2 = length^2 + width^2$

$d^2 = 15^2 + 7^2$

$d^2 = 225 + 49$

$d^2 = 274$

$d = \sqrt{274}$

3. Approximate the square root and round to the nearest tenth

$d \approx 16.5529453583...$

Rounding to the nearest tenth, we get $d \approx 16.6$ units.