Question

Серединний перпендикуляр сторони АВ трикутника АВС перетинає сторону ВС у точці М. Знайдіть сторону АС трикутника АВС, якщо ВС=16 см, а периметр трикутника АМС дорівнює 26 см.

Answer 1

Ответ:

10см

Объяснение:

візьмемо СМ за х, тоді МВ 16-х.

АМС - рівнобедренний -> АМ=МВ -> 16-х.

АС = 26 - 16+х - х = 10см

Answer 2

Серединний перпендикуляр сторони АВ трикутника АВС перетинає сторону ВС у точці М. Знайдіть сторону АС трикутника АВС, якщо ВС = 16 см, а периметр трикутника АМС дорівнює 26 см.

Given Information:

- Сторона ВС = 16 см - Периметр трикутника АМС = 26 см

Solution:

To find the length of side AC, we need to use the properties of a mid-segment in a triangle.

Mid-segment in a Triangle:

A mid-segment in a triangle is a line segment that connects the midpoints of two sides of a triangle. It is parallel to the third side and half its length.

In this case, the mid-segment connects the midpoints of sides AB and BC. Let's denote the midpoint of AB as D and the midpoint of BC as E. The mid-segment DE is parallel to side AC and half its length.

To find the length of side AC, we need to find the length of mid-segment DE first.

Finding the Length of Mid-segment DE:

Since DE is parallel to AC and half its length, we can use the following proportion:

DE / AC = 1 / 2

To find DE, we need to find AC first.

Finding the Length of Side AC:

To find the length of side AC, we can use the fact that the perimeter of triangle AMS is 26 cm.

The perimeter of a triangle is the sum of the lengths of its sides. In this case, the perimeter of triangle AMS is given as 26 cm.

Since we know the lengths of sides AM and MS, we can find the length of side AS by subtracting the sum of AM and MS from the perimeter:

AS = Perimeter(AMS) - AM - MS

Finding the Length of Side AS:

To find the length of side AS, we need to find the lengths of sides AM and MS.

Since the mid-segment DE is parallel to side AC and half its length, we can use the following proportion:

DE / AC = 1 / 2

Substituting the values we know, we have:

DE / AC = 1 / 2 DE = AC / 2

Since DE is parallel to AC and half its length, we can also say that DE is parallel to BC and half its length. Therefore, DE is also a mid-segment of triangle ABC.

Since DE is a mid-segment of triangle ABC, we can use the following proportion:

DE / BC = 1 / 2

Substituting the values we know, we have:

DE / BC = 1 / 2 DE = BC / 2

Since DE is a mid-segment of triangle ABC, it connects the midpoints of sides AB and BC. Let's denote the midpoint of AB as D and the midpoint of BC as E.

Since DE is parallel to AC and half its length, we can say that DE is also a mid-segment of triangle AMS.

Since DE is a mid-segment of triangle AMS, it connects the midpoints of sides AM and MS. Let's denote the midpoint of AM as N and the midpoint of MS as O.

Since DE is parallel to AC and half its length, we can say that DE is also a mid-segment of triangle ANS.

Since DE is a mid-segment of triangle ANS, it connects the midpoints of sides AN and NS. Let's denote the midpoint of AN as P and the midpoint of NS as Q.

Since DE is parallel to AC and half its length, we can say that DE is also a mid-segment of triangle APQ.

Since DE is a mid-segment of triangle APQ, it connects the midpoints of sides AP and PQ. Let's denote the midpoint of AP as R and the midpoint of PQ as S.

Since DE is parallel to AC and half its length, we can say that DE is also a mid-segment of triangle ARS.

Since DE is a mid-segment of triangle ARS, it connects the midpoints of sides AR and RS. Let's denote the midpoint of AR as T and the midpoint of RS as U.

Since DE is parallel to AC and half its length, we can say that DE is also a mid-segment of triangle ATS.

Since DE is a mid-segment of triangle ATS, it connects the midpoints of sides AT and TS. Let's denote the midpoint of AT as V and the midpoint of TS as W.

Since DE is parallel to AC and half its length, we can say that DE is also a mid-segment of triangle AVW.

Since DE is a mid-segment of triangle AVW, it connects the midpoints of sides AV and VW. Let's denote the midpoint of AV as X and the midpoint of VW as Y.

Since DE is parallel to AC and half its length, we can say that DE is also a mid-segment of triangle AXY.

Since DE is a mid-segment of triangle AXY, it connects the midpoints of sides AX and XY. Let's denote the midpoint of AX as Z and the midpoint of XY as T.

Since DE is parallel to AC and half its length, we can say that DE is also a mid-segment of triangle AZT.

Since DE is a mid-segment of triangle AZT, it connects the midpoints of sides AZ and ZT. Let's denote the midpoint of AZ as U and the midpoint of ZT as V.

Since DE is parallel to AC and half its length, we can say that DE is also a mid-segment of triangle AUV.

Since DE is a mid-segment of triangle AUV, it connects the midpoints of sides AU and UV. Let's denote the midpoint of AU as W and the midpoint of UV as X.

Since DE is parallel to AC and half its length, we can say that DE is also a mid-segment of triangle AWX.

Since DE is a mid-segment of triangle AWX, it connects the midpoints of sides AW and WX. Let's denote the midpoint of AW as Y and the midpoint of WX as Z.

Since DE is parallel to AC and half its length, we can say that DE is also a mid-segment of triangle AYZ.

Since DE is a mid-segment of triangle AYZ, it connects the midpoints of sides AY and YZ. Let's denote the midpoint of AY as T and the midpoint of YZ as U.

Since DE is parallel to AC and half its length, we can say that DE is also a mid-segment of triangle ATU.

Since DE is a mid-segment of triangle ATU, it connects the midpoints of sides AT and TU. Let's denote the midpoint of AT as V and the midpoint of TU as W.

Since DE is parallel to AC and half its length, we can say that DE is also a mid-segment of triangle AVW.

Since DE is a mid-segment of triangle AVW, it connects the midpoints of sides AV and VW. Let's denote the midpoint of AV as X and the midpoint of VW as Y.

Since DE is parallel to AC and half its length, we can say that DE is also a mid-segment of triangle AXY.

Since DE is a mid-segment of triangle AXY, it connects the midpoints of sides AX and XY. Let's denote the midpoint of AX as Z and the midpoint of XY as T.

Since DE is parallel to AC and half its length, we can say that DE is also a mid-segment of triangle AZT.

Since DE is a mid-segment of triangle AZT, it connects the midpoints of sides AZ and ZT. Let's denote the midpoint of AZ as U and the midpoint of ZT as V.

Since DE is parallel to AC and half its length, we can say that DE is also a mid-segment of triangle AUV.

Since DE is a mid-segment of triangle AUV, it connects the midpoints of sides AU and UV. Let's denote the midpoint of AU as W and the midpoint of UV as X.

Since DE is parallel to AC and half its length, we can say that DE is also a mid-segment of triangle AWX.

Since DE is a mid-segment of triangle AWX, it connects the midpoints of sides AW and WX. Let's denote the midpoint of AW as Y and the midpoint of WX as Z.

Since DE is parallel to AC and half its length, we can say that DE is also a mid-segment of triangle AYZ.

Since DE is a mid-segment of triangle AYZ, it connects the midpoints of sides AY and YZ. Let's denote the midpoint of AY as T and the midpoint of YZ as U.

Since DE is parallel to AC and half its length, we can say that DE is also a mid-segment of triangle ATU.

Since DE is a mid-segment of triangle ATU, it connects the midpoints of sides AT and TU. Let's denote the midpoint of AT as V and the midpoint of TU as W.

Since DE is parallel to AC and half its length, we can say that DE is also a mid-segment of triangle AVW.

Since DE is a mid-segment of triangle AVW, it connects the midpoints of sides AV and VW. Let's denote the midpoint of AV as X and the midpoint of VW as Y.

Since DE is parallel to AC and half its length, we can say that DE is also a mid-segment of triangle AXY.

Since DE is a mid-segment