Answer:
To find the area of a rectangle when its length and diagonal are given, we can use the Pythagorean theorem to calculate the width of the rectangle.
Let:
Length of the rectangle = 144 cm
Length of the diagonal = 145 cm
Width of the rectangle = ?
According to the Pythagorean theorem, in a right triangle, the square of the hypotenuse (diagonal in this case) is equal to the sum of the squares of the other two sides (length and width in this case).
So, we have:
Diagonal^2 = Length^2 + Width^2
Substitute the given values:
145^2 = 144^2 + Width^2
Solve for Width^2:
Width^2 = 145^2 - 144^2
Width^2 = 21025 - 20736
Width^2 = 289
Take the square root of both sides to find the width:
Width = √289
Width = 17 cm
Now that we have the width, we can calculate the area of the rectangle:
Area = Length × Width
Area = 144 cm × 17 cm
Area = 2448 cm²
Therefore, the area of the rectangle is 2448 square centimeters.