The diagonal of the rectangle is 52 mm and the sides are 5 to 12. find its perimeter.
| June 15, 2021 | education
1. Vertices of the rectangle A, B, C, D. P is the perimeter of the rectangle.
2.CD: AD = 5: 12.
CD = 5AD / 12 centimeters.
3. To calculate the lengths of the sides of a rectangle, we use the formula for calculating its diagonal using the Pythagorean theorem:
AC² = AD² + CD².
AD² + CD² = 2704.
AD² + (5AD / 12) ² = 2704.
25AD² / 144 + AD² = 2704.
169AD² = 2704 x 144.
AD² = 16 x 144.
AD = √16 x 144 = 48 centimeters.
CD = 5AD / 12 = 5 x 48: 12 = 20 centimeters.
P = 2 (CD + AD) = 2 x 68 = 136 centimeters.
Answer: P = 136 centimeters.
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