One side of the rectangle is 5 cm larger than the other and its perimeter is 26 cm

| May 17, 2021 | education

One side of the rectangle is 5 cm larger than the other and its perimeter is 26 cm, find the side of the square whose area is equal to the area of this rectangle.

1) Let the smaller side of the rectangle be equal to x (x) cm, then its second side is equal to: (x + 5) cm.Using the formula for the perimeter of the rectangle ((P = (a + b) 2), we compose the equation:

(x + x + 5) * 2 = 26;

x * 4 + 10 = 26;

x * 4 = 26 – 10;

x * 4 = 16;

x = 16: 4;

x = 4 (cm) – one side of the rectangle.

2) Let’s calculate what the second side of the rectangle is equal to: x + 5 = 4 + 5 = 9 (cm).

3) Calculate the area of a rectangle (and by the condition of the problem and the area of a square) by the formula: S = a * b = 4 * 9 = 36 (cm²).

4) Find out what the size of the side of the square is equal to: a = √S = √36 = 6 (cm).

Answer: the side of the square is 6 cm.



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