Question

A triangle with a perimeter of 24 cm has an altitude of 12 cm and a perimeter of 20 cm divided into two triangles. Find the length of the median

Answer 1

the length of the median of the triangle is 6√(5) cm.

Step-by-step explanation:We can start by using the Pythagorean theorem to find the length of the base of the triangle. Since the altitude of the triangle is 12 cm, the length of the median that divides the triangle into two smaller triangles with perimeter 20 cm can be found using the Pythagorean theorem as follows:

Let's call the length of the base "b". Then, the length of the median "m" is equal to the square root of the sum of the squares of half the base and the height:

m = √((b/2)^2 + 12^2)

We know the perimeter of the triangle is 24 cm, so:

b + 2m = 24

We can substitute b = 24 - 2m into the equation for m:

m = √(((24 - 2m)/2)^2 + 12^2)

Expanding and simplifying the equation gives:

m = √(6^2 + 12^2) = √(36 + 144) = √(180) = 6√(5) cm

So the length of the median of the triangle is 6√(5) cm.