In a rectangle, the sum of some two sides is 9.5 cm, and the sum of some three sides is 7.5 cm. Find the perimeter of this rectangle.
Let’s denote the length and width of this rectangle through A and B.
By the condition of the problem, it is known that the sum of some three sides is 7.5 cm.
Since the lengths of the four sides of the triangle are A, B, A, B, we can write the equation:
2 * A + B = 7.5.
It is also known that the sum of some two sides is 9.5 cm.
Note that the possible options for choosing two sides: A and A, B and B, A and B.
If it is A and B, then A + B = 9.5. But A + B = 9.5 <2 * A + B = 7.5. This option is not possible.
If it is A and A, then A + A = 2 * A = 9.5 <2 * A + B = 7.5. This option is also impossible.
There remains only option B and B.
B + B = 9.5,
B = 9.5 / 2.
Therefore, the perimeter P of this rectangle is:
P = 2 * (A + B) = 2 * A + B + B = 7.5 + 9.5 / 2 = 24.5 / 2 = 12.25.