Find the area of the rectangle if the perimeter of the rectangle is 20 cm and the length is 6 cm, change the sides so

| June 22, 2021 | education

Find the area of the rectangle if the perimeter of the rectangle is 20 cm and the length is 6 cm, change the sides so that the perimeter does not change and the area becomes 16 m2.

1) Let a = 6 cm, and the perimeter 2 * (a + b) = 20 cm, or (a + b) = 20/2 = 10 cm, whence b = 10 – a = 10 – 6 = 4 (cm) … Then the area c = a * b = 6 cm * 4 cm = 24 cm ^ 2.

2) Without changing the perimeter p = 20 cm = 2 * (a1 + b1), and (a1 + b1) = 10 cm, we determine its area c1 = a1 * b1 = 16 cm2.

Let’s make the equation: a1 = 10 – b1, then a1 * b1 = b1 * (10 – b1) = 16. Let’s open the brackets:

10 * в1 – (в1) ^ 2 = 16, whence: (в1) ^ 2 – 10 * в1 + 16 = 0. Find the root в1 = 10/2 + – √ (5 ^ 2 – 16) = 5 + – √ (25 – 16) = 5 + – √9 = 5 + -3. b1 = 8, a1 = 2, c1 = 16 cm ^ 2.



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