Answer:
To find the area of a rectangle when its length and diagonal are given, we can use the following approach:
Let's denote the width of the rectangle as "w."
We know that the length (L), width (w), and diagonal (d) of a rectangle form a right triangle where the diagonal is the hypotenuse. Therefore, we can use the Pythagorean theorem:
d² = L² + w²
Given:
Length (L) = 144 cm
Diagonal (d) = 145 cm
Now, plug in the values and solve for the width (w):
145² = 144² + w²
21025 = 20736 + w²
w² = 21025 - 20736
w² = 289
Take the square root of both sides to find the width (w):
w = √289
w = 17 cm
Now that we have the width, we can calculate the area (A) of the rectangle using the formula:
A = Length × Width
A = 144 cm × 17 cm
A = 2448 cm²
Therefore, the area of the rectangle is 2448 square centimeters.