Question

Периметр четырехугольника равен 52 см . одна его сторона равна 1дм 4 см , вторая на 5 см меньше первой , а третья на 8 см больше второй . найдите длину четвертой стороны?Помогите пожалуйста решить задачу.

Answer 1

1 строна= 14см
2 сторона  14-5=9 см
3 сторона 9+8=17 см
52-14-9-17=12см-длина четвертой стороны

Answer 2

Краткая запись:
Дано_
P=52см
1ст=14см
2ст=14-5
3ст=14+8
_________________________
1)14-5=9(см) 2-ая сторона
2)14+8=22(см) 3-я сторона
3)58-(14+9+22)=58-45=13(см) 4-ая сторона

Answer 3

Problem Analysis

We are given the perimeter of a quadrilateral, which is 52 cm. We are also given the lengths of three sides of the quadrilateral: one side is 1 dm 4 cm, the second side is 5 cm shorter than the first side, and the third side is 8 cm longer than the second side. We need to find the length of the fourth side.

Solution

Let's denote the length of the first side as a, the length of the second side as b, the length of the third side as c, and the length of the fourth side as d.

We are given the following information: - The perimeter of the quadrilateral is 52 cm, so we can write the equation: a + b + c + d = 52.- The length of the first side is 1 dm 4 cm, which is equal to 14 cm. - The second side is 5 cm shorter than the first side, so we can write: b = a - 5. - The third side is 8 cm longer than the second side, so we can write: c = b + 8.

To find the length of the fourth side, we need to substitute the values of a, b, and c into the equation a + b + c + d = 52 and solve for d.

Let's solve the equations step by step:

1. Substitute b = a - 5 into the equation c = b + 8 to get c = (a - 5) + 8. 2. Substitute c = (a - 5) + 8 into the equation a + b + c + d = 52 to get a + (a - 5) + ((a - 5) + 8) + d = 52. 3. Simplify the equation: 3a - 2 + d = 52. 4. Rearrange the equation to solve for d: d = 52 - 3a + 2.

Now, we can substitute the value of a (14 cm) into the equation d = 52 - 3a + 2 to find the length of the fourth side d.

Calculation

Substituting a = 14 into the equation d = 52 - 3a + 2, we get:

d = 52 - 3(14) + 2.

Simplifying the equation, we have:

d = 52 - 42 + 2.

d = 12.

Therefore, the length of the fourth side is 12 cm.

Answer

The length of the fourth side of the quadrilateral is 12 cm.