ABC is an isoscele triangle in which [AB]=[AC]=5cm and [BC]=6cm. Calculate [AM], where M is the mid-point of BC.
4cm
In order to find the length of [AM], you want to look at only half of this triangle. Half of an isosceles triangle is a right angle triangle! Therefore you can use Pythagorean theory:
a^2 + b^2 = c^2 (hypotenuse)
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Pls i need the answer urgently
To calculate the length of [AM], we can use the property of an isosceles triangle, which states that the distance from the vertex of the triangle to the midpoint of the base is the height or altitude of the triangle.
In this case, since M is the midpoint of BC, we can draw a perpendicular line from A to the line BC, intersecting it at point D.
To find the length of [AM], we need to find the length of AD, which is the altitude of the triangle.
Since ABC is an isosceles triangle, we know that AD is also the perpendicular bisector of the base.
To find the length of AD, we can use the Pythagorean theorem. According to the theorem, in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In triangle ADB, we have AB = 5 cm and BD = BC/2 = 6/2 = 3 cm (as M is the midpoint of BC).
Using the Pythagorean theorem, we can solve for AD:
AD^2 = AB^2 - BD^2
AD^2 = 5^2 - 3^2
AD^2 = 25 - 9
AD^2 = 16
AD = √16
AD = 4 cm
Therefore, the length of [AM] is equal to the length of [AD], which is 4 cm.