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. 

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.

To find the length of the diagonal of a rectangle, you can use the Pythagorean theorem. In a rectangle, the diagonal, width, and length form a right triangle.

Given:

Area of the rectangle = 105 square units

Width = 7 units

Let the length of the rectangle be "l".

Since the area of a rectangle is given by the formula:

Area = length × width

105 = l × 7

l = 105/7

l = 15

Now, we have the length (l) and the width (w) of the rectangle. We can find the diagonal (d) using the Pythagorean theorem:

d^2 = l^2 + w^2

d^2 = 15^2 + 7^2

d^2 = 225 + 49

d^2 = 274

Now, we take the square root of both sides to find d:

d = √274

Using a calculator, we find:

d ≈ 16.55

Rounding to the nearest tenth, the length of the diagonal of the rectangle is approximately 16.6 units.

How to Calculate the Area and Perimeter of a Rectangle?

To calculate the area and perimeter of a rectangle, you need to know the length and width of the rectangle.

1. Area of a Rectangle: The area (A) of a rectangle is given by the formula: A = Length × Width

2. Perimeter of a Rectangle: The perimeter (P) of a rectangle is given by the formula: P = 2 × (Length + Width)

Here's how to calculate:

Example: Let's say you have a rectangle with a length of 6 units and a width of 4 units.

1. Area: A = 6 × 4 = 24 square units So, the area of the rectangle is 24 square units.

2. Perimeter: P = 2 × (6 + 4) = 2 × 10 = 20 units So, the perimeter of the rectangle is 20 units.

That's it! You've calculated the area and perimeter of a rectangle. Just plug in the values of length and width into the respective formulas, and you can find the area and perimeter of any rectangle.