Let us denote the lengths of the sides of this rectangle through x and y.
According to the condition of the problem, the perimeter of this rectangle is 36 cm, therefore, we can write the following relationship:
2 * (x + y) = 36.
It is also known that the sum of the lengths of the three sides of this rectangle is 25 cm, therefore, we can write the following ratio:
x + y + x = 25.
We solve the resulting system of equations.
Subtracting the second equation from the first, we get:
2 * (x + y) – 2x – y = 36 – 25;
2x + 2y – 2x – y = 11;
y = 11 cm.
Substituting the found value y = 11 into the equation 2x + y = 25, we get:
2x + 11 = 25;
2x = 25 – 11;
2x = 14;
x = 14/2;
x = 7 cm.
Find the area of the rectangle:
11 * 7 = 77 sq. cm.
Answer: the area of the rectangle is 77 square meters. cm.
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