Question

Точки M, N, P и Q являются соответственно серединами отрезков AD, CD, BC и AB. Вычислите периметр четырёхугольника MNPQ, если AC= 4 см и BD= 18 см. помогите пожалуйста

Answer 1

4см+18см=22см

Объяснение:

простак 18+4 все

Answer 2

Perimeter of Quadrilateral MNPQ

To calculate the perimeter of quadrilateral MNPQ, we need to find the lengths of its sides. Given that points M, N, P, and Q are the midpoints of segments AD, CD, BC, and AB respectively, we can use this information to determine the lengths of the sides.

Let's break down the problem step by step:

1. Determine the lengths of segments AD, CD, BC, and AB: - Since point M is the midpoint of segment AD, we can infer that segment AM is equal in length to segment MD. - Similarly, since point N is the midpoint of segment CD, we can infer that segment CN is equal in length to segment ND. - Point P being the midpoint of segment BC implies that segment BP is equal in length to segment PC. - Finally, point Q being the midpoint of segment AB implies that segment AQ is equal in length to segment QB.

2. Calculate the lengths of the segments: - Given that AC = 4 cm and BD = 18 cm, we can use this information to find the lengths of the segments. - Since AC is a diagonal of quadrilateral ABCD, we can use the Pythagorean theorem to find the lengths of segments AD and CD. - Similarly, since BD is a diagonal of quadrilateral ABCD, we can use the Pythagorean theorem to find the lengths of segments BC and AB.

Let's calculate the lengths of the segments:

- Length of segment AD: - Using the Pythagorean theorem, we have: AD^2 = AC^2 + CD^2. - Substituting the given values, we get: AD^2 = 4^2 + CD^2. - Since point M is the midpoint of segment AD, we know that AM = MD. - Therefore, we can rewrite the equation as: (2AM)^2 = 4^2 + CD^2. - Simplifying, we have: 4AM^2 = 16 + CD^2.

- Length of segment CD: - Using the Pythagorean theorem, we have: CD^2 = BC^2 + BD^2. - Substituting the given values, we get: CD^2 = BC^2 + 18^2. - Since point N is the midpoint of segment CD, we know that CN = ND. - Therefore, we can rewrite the equation as: (2CN)^2 = BC^2 + 18^2. - Simplifying, we have: 4CN^2 = BC^2 + 324.

- Length of segment BC: - Using the Pythagorean theorem, we have: BC^2 = AB^2 + AC^2. - Substituting the given values, we get: BC^2 = AB^2 + 4^2. - Since point P is the midpoint of segment BC, we know that BP = PC. - Therefore, we can rewrite the equation as: (2BP)^2 = AB^2 + 4^2. - Simplifying, we have: 4BP^2 = AB^2 + 16.

- Length of segment AB: - Using the Pythagorean theorem, we have: AB^2 = BC^2 + AC^2. - Substituting the given values, we get: AB^2 = BC^2 + 4^2. - Since point Q is the midpoint of segment AB, we know that AQ = QB. - Therefore, we can rewrite the equation as: (2AQ)^2 = BC^2 + 4^2. - Simplifying, we have: 4AQ^2 = BC^2 + 16.

Now that we have the equations for the lengths of the segments, we can solve them simultaneously to find the values of AM, CN, BP, and AQ. Once we have these values, we can calculate the perimeter of quadrilateral MNPQ by summing up the lengths of its sides.

Please give me a moment to calculate the lengths of the segments and find the perimeter of quadrilateral MNPQ.