The diagonal of a rectangle is 24 inches. The width is 15 inches. What is the area?
A = 45 radical 39
Correct
To find the area of a rectangle, you need to know either the length and width or the length of a diagonal. In this case, you are given the width and the length of a diagonal.
Let's denote the length of the rectangle as 'L'. We can use the Pythagorean theorem to find the length of the rectangle:
According to the Pythagorean theorem, in a right-angled triangle, the square of the hypotenuse (the diagonal in this case) is equal to the sum of the squares of the other two sides (the length and width of the rectangle).
So, we have the equation:
L^2 + 15^2 = 24^2
Simplifying the equation:
L^2 + 225 = 576
Subtracting 225 from both sides:
L^2 = 351
Taking the square root of both sides:
L = √351
Now, to find the area of the rectangle, you multiply the length by the width:
Area = L * 15
Plugging in the value of L:
Area = √351 * 15
Calculating the approximate value:
Area ≈ 18.71 * 15
Area ≈ 280.65 square inches
Therefore, the area of the rectangle is approximately 280.65 square inches.