Find the altitude of a triangle with sides 5, 5, and 6?

Answer 1

Hint: in an isosceles triangle, the altitude (perpendicular) from the vertex angle is also a median (crosses the midpoint). Then you use Pythagorean theorem to find the altitude since you've created two right triangles.

Answer 2

Since there are two sides of length 5, the triangle must be isosceles with legs of length 5 and a base of length 6.

Draw the altitude from the vertex angle of this isosceles triangle. That altitude will divide the triangle into two smaller, congruent right triangles. Since the right triangles are congruent, you have a leg of length 3 in each right triangle as well as a hypotenuse of length 5.

Use the Pythagorean theorem to find the length of the altitude. OR, if you know your Pythagorean triples, you know that a right triangle with a hypotenuse of 5 and a leg of 3 has another leg of length 4.

However, there is a second altitude to the triangle: the perpendicular segment drawn from one of the base vertices to the opposite leg. I don't imagine that they want that segment, but technically, all triangles have three altitudes.

Answer 3

if the base is "5" then the altitude is "5"
but is the base is "6" then the sltitude is "4" by applying the properties of an isosceles triangles and the Pythagorean theorem..
6/2 = 3
5^2 = x^2 + 3^2
x = 4 = altitude

Answer 4

A triangle with those measurements has to be isosceles, with the base being 6 units and the sides being 5.

That means it can be divided into two right triangles with sides 3 and x units, x being the altitude of the original triangle, and a hypotenuse of 5 units.

3 squared + x squared = 5 squared
9 + x squared =25
x squared = 16
x = square root of 16
x = 4

Answer 5

4 is indeed the answer the textbook and the teacher expects.

However, that assumes the altitude being found is the one that intersects the side of 6.

Nothing in the statement of the problem says that.

If the altitude being found is the one that intersects one of the sides of 5, then the answer is no longer 4.

Answer 6

you can show that this is isosceles
and therefore, you can say that the altitude is perpendicular and a segment bisector of the opposite side

then you have two triangles with sides 3, _, 5
you can use pythagorean triples
since 3,4,5 is a pythagorean triple, you then know that the missing side is 4

and then the altitude is 4

Answer 7

4

Because this trigle is an isosceles triangle.
The height bisects the base. half base=6/2=3
Right angled triangle 3,4,5

Hence the height is 4