Question

Диагонали прямоугольника ABCD ПЕРЕСЕКАЮТСЯ В ТОЧКЕ М , АВ=7, АС=12. Найдите периметр треугольника АВМ

Answer 1

AM=MC=12
AM=6
BA=7
BM=12-5
BM=7+6+5=18см

Answer 2

Finding the Perimeter of Triangle ABM

To find the perimeter of triangle ABM, we can use the given information about the diagonals of rectangle ABCD and the length of sides AB and AC.

Given: - Diagonals of rectangle ABCD intersect at point M. - AB = 7 - AC = 12

Solution

First, let's find the length of the diagonal BD of the rectangle using the given information.

The diagonals of a rectangle are equal in length, so we can use this property to find the length of BD.

The length of BD can be found using the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Using the Pythagorean theorem: BD^2 = AB^2 + AC^2 BD^2 = 7^2 + 12^2 BD^2 = 49 + 144 BD^2 = 193 BD = √193

Now that we have the length of BD, we can find the perimeter of triangle ABM by adding the lengths of sides AB, BM, and AM.

The length of BM and AM can be found using the properties of diagonals in a rectangle.

BM = AM = 0.5 * BD

Now, we can calculate the perimeter of triangle ABM: Perimeter = AB + BM + AM Perimeter = AB + 0.5 * BD + 0.5 * BD Perimeter = 7 + 0.5 * √193 + 0.5 * √193 Perimeter = 7 + √193

The perimeter of triangle ABM is 7 + √193.