The perimeter of the rectangle is 24 cm, and its area is 32 cm2. Determine what is the length and width of the rectangle?

| June 20, 2021 | education

P rectangle = 2 * (a + b), S rectangle = a * b, where a and b are the length and width of the rectangle. Consider the formula for the perimeter of a given rectangle, we get: 24 = 2 * (a + b). a + b = 24: 2. a + b = 12. a = 12-b. Substitute this value “a” in the formula for the area of ​​a rectangle, we get: S rectangle = (12-b) * b. 32 = (12-b) * b. 32 = 12 * b-b * b. 32 = 12b-b ^ 2. We transfer the number (32) to the right side, we get: 12b-b ^ 2-32 = 0. D = b ^ 2-4 * a * c. D = 12 ^ 2-4 * (- 1) * (- 32). D = 144-4 * 32. D = 144-128. D = 16. Root of D = 4. x1,2 = (-b + -root of D) / 2 * a. x1,2 = (-12 + -4) / – 2. x1,2 = (12 + -4) / 2. x1 = (12 + 4) / 2. x1 = 16/2. x1 = 8. 8 (cm) – the length of the rectangle. x2 = (12-4) / 2. x2 = 8/2. x2 = 4. 4 (cm) – the width of the rectangle. Check: S = a * b, 32 = 8 * 4. 32 = 32, so it is true.
Answer: 8 cm and 4 cm.



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