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 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.
Calculate the diagonal length of a rectangle with an area of 105 square units and width measuring 7 units. Find your answer rounded to the nearest tenth here!
by Maivizhi A
Updated Mar 05, 2024
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.

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

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.

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

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.
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  FAQs
1. What is the formula to find the length of the diagonal of a rectangle?
The length of the diagonal of a rectangle can be found using the Pythagorean theorem: d^2 = l^2 + w^2, where d is the diagonal, l is the length, and w is the width.
2. Why do we use the Pythagorean theorem to find the diagonal of a rectangle?
In a rectangle, the diagonal, length, and width form a right triangle. The Pythagorean theorem applies to right triangles, making it suitable for finding the diagonal.
3. What information do we need to find the diagonal of a rectangle?
You need to know the area of the rectangle and the width to find the length of the diagonal.
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