The perimeter of the rectangle is AB = 62 cm, AB = 12 cm, AB = CA. Find the length of side AB

| August 17, 2021 | education

Apparently, a mistake was made in the formulation of the task. If it is necessary to find the length of the side AB, then we will assume that the length of the side BC = 12 cm is given. Then, under other conditions, the task is solved correctly.
As you know, the sum of the lengths of all sides is called the perimeter of a triangle. If the perimeter of the rectangle ABC is 62 cm, then AB + BC + CA = 62 cm.
To find the length of the side AB. Let’s use another condition of the task. Since, according to the condition of the task, AB = CA, then substituting this and BC = 12 cm into the equality from item 1, we get: AB + 12 cm + AB = 62 cm or 2 * AB = 62 cm – 12 cm = 50 cm, whence AB = (50 cm): 2 = 25 cm.
Checking any condition for the existence of a triangle (for example, the sum of any two sides of a triangle is greater than the third side) confirms that there is a triangle with sides: 12 cm; 25 cm and 25 cm.
Answer: AB = 25 cm.



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