The parallelogram half-perimeter is 26 cm and the sum is 22 cm. Find the sides of the parallelogram?
| April 10, 2021 | education
P / 2 = 26 cm.
a + c = 22 cm.
a -?
b -?
c -?
d -?
1) The perimeter of a parallelogram P is the sum of all its sides: P =
a + b + c + d.
2) According to the property of a parallelogram, its opposite sides are equal to each other: a = c, d = b.
The perimeter P will be determined by the formula:
P = a + b + a + b = 2 * (a + b).
3) The parallelogram’s semi-perimeter will be the sum of its adjacent sides: Р / 2 = a + b.
4) This means that the sum of 22 cm is the sum of its opposite sides: a + c = 22 cm.
a = c = 11 cm.
5) Find sides d and b.
b = P / 2 – a.
b = d = 26 cm – 11 cm = 15 cm.
Answer: a = c = 11 cm, b = d = 15 cm.
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