The area of the rectangle is 15cm2, and the sum of its legs is 11cm. Find legs.

| September 17, 2021 | education

We will solve the problem using conditional variables “X” and “Y”, which will be equal to the values ​​of the legs of the rectangle.

Given the information in this example, we compose the following equations:

1) X x Y = 2 x 15;

2) X + Y = 11.

As a result of solving this system of equations, we obtain X = 11 – Y.

Substituting X in the first equation, we have (11 – Y) x Y = 30 or 11Y – Y ^ 2 = 30 or Y ^ 2 – 11Y + 30 = 0.

Solving the quadratic equation, we have the following roots Y1 = (- (- 11) + √ ((- 11) ^ 2 – 4 x 1 x 30)) / 2 x 1 = (11 + √ (121 – 120)) / 2 = (11 + 1) / 2 = 12/2 = 6 centimeters and Y2 = (- (- 11) – √ ((- 11) ^ 2 – 4 x 1 x 30)) / 2 x 1 = (11 – √ ( 121 – 120)) / 2 = (11 – 1) / 2 = 10/2 = 5 centimeters.

Accordingly, X1 = 11 – 6 = 5 centimeters and X2 = 11 – 5 = 6 centimeters.

Answer: the legs are 5 and 6 centimeters.



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