The rectangle has a perimeter of 40 and an area of 75. Find the larger side of the rectangle.

univerkov | July 24, 2021 | education

Since ABCD is a rectangle, then AB = CD, BC = AD.

Then Savsd = AB * AD = 75 cm2. (one)

Ravsd = 2 * (AB + AD) = 40 cm. (2)

Let’s solve the system of equations 1 and 2.

AB = 75 / AD.

2 * (75 / AD + AD) = 40.

AD + 75 / AD = 20.

AD ^ 2 + 75 = 20 * AD.

AD ^ 2 – 20 * AD + 75 = 0.

Let’s solve the quadratic equation.

AD1 = 5 cm.

AD2 = 15 cm.

15> 5, then AD = 15 cm.

Answer: The length of the longer side is 15 cm.

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