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The area of a rectangle is 99 square units. Its width measures 11 units. Find the length of its diagonal. Round to the nearest tenth of a unit.
The length of the diagonal of the rectangle, rounded to the nearest tenth of a unit, is approximately 14.2 units.
To find the length of the diagonal of a rectangle, we can use the Pythagorean theorem. Let’s denote the length of the rectangle as “l” (in this case, “l” represents the unknown length) and the width as “w” (given as 11 units). According to the Pythagorean theorem:
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Diagonal^2 = Length^2 + Width^2
Given that the area of the rectangle is 99 square units and the width is 11 units, we can find the length:
Area = Length × Width
99 = l × 11
l = 99/11
l = 9
So, the length of the rectangle is 9 units.
Now, we can find the length of the diagonal:
Diagonal^2 = 9^2 + 11^2
Diagonal^2 = 81 + 121
Diagonal^2 = 202
Taking the square root of both sides:
Diagonal = √202
Rounding to the nearest tenth of a unit:
Diagonal ≈ 14.2
So, the length of the diagonal of the rectangle, rounded to the nearest tenth of a unit, is approximately 14.2 units.
Area and Perimeter of a Rectangle
To find the area and perimeter of a rectangle, you’ll need to know the length and width of the rectangle.
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Area of a Rectangle: The area (A) of a rectangle is calculated by multiplying its length (l) by its width (w): A = l * w
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Perimeter of a Rectangle: The perimeter (P) of a rectangle is the sum of all its sides. For a rectangle with length l and width w, the perimeter is: P = 2l + 2w
So, if you have the length and width of the rectangle, you can easily calculate its area and perimeter using these formulas.
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