To find the length of the diagonal of the rectangle, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (in this case, the diagonal) is equal to the sum of the squares of the other two sides.
Given:
Area of the rectangle = 110 square units
Length of the rectangle = 11 units
1. First, we need to find the width of the rectangle using the formula for the area of a rectangle:
Area = Length x Width
110 = 11 x Width
Width = 110 / 11
Width = 10 units
2. Now that we have the length (11 units) and width (10 units) of the rectangle, we can find the length of the diagonal using the Pythagorean theorem:
Diagonal^2 = Length^2 + Width^2
Diagonal^2 = 11^2 + 10^2
Diagonal^2 = 121 + 100
Diagonal^2 = 221
3. Taking the square root of both sides to find the length of the diagonal:
Diagonal = √221
Diagonal ≈ 14.9 units
Therefore, the length of the diagonal of the rectangle is approximately 14.9 units when rounded to the nearest tenth of a unit.
