the base of an isoscels triangle is 4x long. the altitude to the base is 3x cm long. Find the length of one other side of the triangle

Half base = 4x/2=2x

altitude =3x
Half of an isosceles triangle is a right triangle, so use Pythagoras theorem to get
Other side = √((2x)^2+(3x)^2)
=(√13)x

To find the length of one of the other sides of the isosceles triangle, we can use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In an isosceles triangle, the two equal sides are also the legs of a right triangle formed by dropping an altitude from the vertex to the base. Let's denote the length of the base as 4x and the length of the altitude as 3x.

Using the Pythagorean Theorem, we have:

(One side of the triangle)^2 = (Length of one leg)^2 + (Length of the altitude)^2

Let's denote the length of one side of the triangle as s. In this case, we want to find the value of s.

s^2 = (4x)^2 + (3x)^2
s^2 = 16x^2 + 9x^2
s^2 = 25x^2

To find the length of one side of the triangle, we take the square root of both sides:

s = √(25x^2)
s = 5x

Therefore, the length of one of the other sides of the triangle is 5x.