abc is an isosceles triangle in which ab=ac=5cm and BC =6cm.calculate \am\where m is the midpoint of BC
If you make your sketch, you should realize that you have
two congruent right-angled triangles with base 3, and hypotenuse 5.
You should recognize the basic 3-4-5 right angled triangle, since
3^2 + 4^2 = 5^2
so AM = 4
To find the length of \am\, we can use the Pythagorean theorem.
First, let's draw a diagram of the triangle ABC.
A
/ \
/ \
/ \
/ \ m
/ \
B-----------C
Since ABC is an isosceles triangle, we know that the base angles at B and C are equal. Let's call them \angle BAC and \angle CAB.
Since AB = AC, we can say that \angle BAC = \angle CAB.
Since ABC is an isosceles triangle, we can also say that BM = CM (M is the midpoint of BC).
Now, let's use the Pythagorean theorem to find the length of \am\.
In triangle ABM, we have:
AB^2 = AM^2 + BM^2
Substituting the known values, we have:
5^2 = AM^2 + (BC/2)^2
Simplifying the equation:
25 = AM^2 + (6/2)^2
25 = AM^2 + 9
AM^2 = 25 - 9
AM^2 = 16
Taking the square root of both sides, we get:
AM = 4 cm
Therefore, the length of \am\ is 4 cm.