Question

2.84 Периметр пятиугольника MNPQs равен 104 см. Стороны MN и MS равны 51 см, сторона NP короче стороны MN на 16 см, но длиннее стороны РQ на 7 см. Найдите сторону МQ. ​

Answer 1

MN=25,5
NP=25,5-16=9,5+7=16,5
PQ=25,5-7=18,5
Mg=104-25,5-16,5-25,5-18,5=18

Answer 2

Problem Analysis

We are given a pentagon MNPQS with a perimeter of 104 cm. The lengths of sides MN and MS are both 51 cm. Side NP is 16 cm shorter than side MN, and side NP is 7 cm longer than side PQ. We need to find the length of side MQ.

Solution

Let's break down the information given: - Perimeter of the pentagon MNPQS = 104 cm. - Length of side MN = 51 cm. - Length of side MS = 51 cm. - Length of side NP is 16 cm shorter than side MN. - Length of side NP is 7 cm longer than side PQ.

To find the length of side MQ, we need to determine the lengths of sides NP and PQ.

Let's assume the length of side NP is x cm. Since side NP is 16 cm shorter than side MN, we can write the equation: x = 51 - 16.

Let's solve for x: x = 51 - 16 x = 35 cm

Now, we know the length of side NP is 35 cm. We also know that side NP is 7 cm longer than side PQ. So, we can write the equation: NP = PQ + 7.

Let's solve for PQ: 35 = PQ + 7 PQ = 35 - 7 PQ = 28 cm

Now, we have the lengths of sides NP and PQ. To find the length of side MQ, we can subtract the lengths of sides NP and PQ from the perimeter of the pentagon.

Perimeter of the pentagon = sum of all side lengths 104 = MN + NP + PQ + QS + SM

Since MN = 51 cm, NP = 35 cm, PQ = 28 cm, MS = 51 cm, and QS = SM, we can rewrite the equation as: 104 = 51 + 35 + 28 + QS + 51

Let's solve for QS: 104 = 51 + 35 + 28 + QS + 51 104 = 165 + QS QS = 104 - 165 QS = -61 cm

Since the length of a side cannot be negative, we made an error in our calculations. Let's review the problem.

Error Analysis

Upon reviewing the problem, we can see that there is an inconsistency in the given information. The length of side NP is stated to be both shorter than side MN by 16 cm and longer than side PQ by 7 cm. However, these two statements contradict each other. It is not possible for side NP to be shorter than side MN by 16 cm and longer than side PQ by 7 cm at the same time.

Therefore, we cannot accurately determine the length of side MQ based on the given information. It is likely that there is an error or inconsistency in the problem statement.

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