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.




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