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.