# The perpendicular dropped from the top of the rectangle divides its diagonal into segments

The perpendicular dropped from the top of the rectangle divides its diagonal into segments of 9 cm and 16 cm. Calculate the area of the rectangle

1. Vertices of the rectangle A, B, C, D. AC – diagonal. BH is the height drawn to the diagonal.

AH = 9 centimeters. CH = 16 centimeters.

2. The length of the height BH, drawn from the vertex of the right angle of the triangle ABC, is calculated

according to the formula:

BH = √AN x CH = √9 x 16 = √144 = 12 centimeters.

3. AC = AH + CH = 9 + 16 = 25 centimeters.

4. Calculate the area of ​​the triangle ABC:

AC x BH / 2 = 25 x 12/2 = 150 centimeters².

5. The diagonal of the rectangle divides it into two equal triangles ABC and ACD.

6. With this in mind, we calculate the area (S) of the rectangle:

S = 150 x 2 = 300 centimeters².

Answer: The area of ​​a rectangle is 300 centimeters².

One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.
The text passage describes a geometric problem involving a rectangle and its diagonal, and it provides a detailed step-by-step solution to calculate the area of the rectangle.
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Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
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# The perpendicular dropped from the top of the rectangle divides its diagonal into segments

The perpendicular dropped from the top of the rectangle divides its diagonal into segments of 9 cm and 16 cm. Calculate the area of the rectangle

1. Vertices of the rectangle A, B, C, D. AC – diagonal. BH is the height drawn to the diagonal.

AH = 9 centimeters. CH = 16 centimeters.

2. The length of the height BH, drawn from the vertex of the right angle of the triangle ABC, is calculated

according to the formula:

BH = √AN x CH = √9 x 16 = √144 = 12 centimeters.

3. AC = AH + CH = 9 + 16 = 25 centimeters.

4. Calculate the area of ​​the triangle ABC:

AC x BH / 2 = 25 x 12/2 = 150 centimeters².

5. The diagonal of the rectangle divides it into two equal triangles ABC and ACD.

6. With this in mind, we calculate the area (S) of the rectangle:

S = 150 x 2 = 300 centimeters².

Answer: The area of ​​a rectangle is 300 centimeters².

One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.
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The text passage describes a geometric problem involving a rectangle and its diagonal, and it provides a detailed step-by-step solution to calculate the area of the rectangle.

TYPE: SINGLE_QUESTION_WITH_ANSWER