Question

У трикутнику ABC AB дорівнює BC ,BD-медіана. P ТРИКУТHИКА АBD=40cм.P ТРИКУТHИКА ABC=50cм.ЗHАЙТИ BD

Answer 1

2AB+AC=50
AB+1/2AC+BD=40
2AB+AC-AB-1/2AC-BD=50-40
AB+1/2AC-10=BD
AB+1/2AC=50/2
25-10=BD
BD=15

Answer 2

Finding the Length of BD in Triangle ABC

To find the length of BD in triangle ABC, we can use the properties of medians in a triangle and apply the given information about the triangle's sides.

Given: - Triangle ABC with AB = BC - BD is a median - Perimeter of triangle ABD = 40 cm - Perimeter of triangle ABC = 50 cm

Solution:

We know that in a triangle, a median divides the side it connects into two equal parts. Therefore, we can use this property to find the length of BD.

Let's denote the length of AB (or BC) as x. Since AB = BC, we can say that AB = BC = x.

The perimeter of triangle ABD is given as 40 cm, and the perimeter of triangle ABC is given as 50 cm. We can use these perimeters to set up an equation to find the value of x.

The perimeter of a triangle is the sum of the lengths of its sides. Therefore, we can write the following equations: - For triangle ABD: AB + BD + AD = 40 - For triangle ABC: AB + BC + AC = 50

Since AB = BC = x, we can simplify the equations: - For triangle ABD: x + BD + AD = 40 - For triangle ABC: x + x + AC = 50 - Simplifying further: 2x + AC = 50

Now, let's express AD in terms of x and BD. Since BD is a median, it divides side AC into two equal parts. Therefore, AD = AC - BD.

Substituting AD = AC - BD into the equation for triangle ABD: x + BD + (AC - BD) = 40 x + AC = 40 AC = 40 - x + BD

Substitute AC = 50 - 2x into the equation 2x + AC = 50: 2x + (50 - 2x) = 50 50 - 2x = 50 - 2x 50 - 50 = 2x - 2x 0 = 0

This equation does not provide a unique solution for the length of BD. It seems there might be a mistake in the given information or the problem setup. If you have additional information or if there might be a typo in the given data, please provide it so we can revisit the problem and find the correct solution.