Question

З вершини кута прямокутника проведений перпендикуляр на діагональ,який ділить діагональ на відрізки 9 та 16 см.Знайти площу прямокутника.

Answer 1

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Answer 2

Finding the Length of the Diagonal

To find the area of a rectangle, we first need to find the length of its diagonal. From the given information, we know that a perpendicular is drawn from the vertex of the angle to the diagonal, dividing it into segments of 9 cm and 16 cm.

Let's denote the length of the shorter segment as 'a' and the length of the longer segment as 'b'. According to the given information, we have:

a = 9 cm b = 16 cm

To find the length of the diagonal, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the diagonal is the hypotenuse, and the two segments are the other two sides of the right triangle. Therefore, we can use the formula:

diagonal^2 = a^2 + b^2

Substituting the given values, we have:

diagonal^2 = 9^2 + 16^2

Simplifying the equation:

diagonal^2 = 81 + 256

diagonal^2 = 337

Taking the square root of both sides, we find:

diagonal ≈ √337 ≈ 18.357 cm

Finding the Area of the Rectangle

Now that we know the length of the diagonal, we can find the area of the rectangle.

The area of a rectangle can be calculated by multiplying the lengths of its two adjacent sides. In this case, the two adjacent sides are the segments of the diagonal.

Let's denote the length of the shorter segment as 'a' and the length of the longer segment as 'b'. From the given information, we have:

a = 9 cm b = 16 cm

To find the area, we can use the formula:

area = a * b

Substituting the given values, we have:

area = 9 cm * 16 cm

Calculating the area:

area = 144 cm^2

Therefore, the area of the rectangle is approximately 144 square centimeters.

Please let me know if there's anything else I can help you with!