the length of the base of a triangle is 4 times its altitude. if the area of a triangles is 162cm2 find the altitude
let altitude be x
area = 1/2 * base * altitude
= 1/2 * x * 4x = 162
x^2 = 81
x=9
so altitude = 9cm
To find the altitude of the triangle, we need to use the formula for the area of a triangle:
Area = (1/2) * base * altitude
Given that the area of the triangle is 162 cm², we can plug in the values and solve for the altitude.
162 = (1/2) * base * altitude
Since the length of the base is 4 times the altitude, we can rewrite the equation as:
162 = (1/2) * (4 * altitude) * altitude
Simplifying further:
162 = 2 * altitude²
Dividing both sides of the equation by 2:
81 = altitude²
Taking the square root of both sides:
√81 = √(altitude²)
Therefore, the altitude of the triangle is ±9 cm.
However, since altitude cannot be negative in this context, the actual altitude is 9 cm.
To find the altitude of a triangle, we need to know the length of its base and its area. In this case, we are given that the length of the base is 4 times the altitude, and the area is 162cm^2.
Let's assume the altitude of the triangle is "h" and the base is "b".
Given: b = 4h (Length of the base is 4 times the altitude)
Given: Area = 162cm^2
We know the formula for the area of a triangle is: Area = (1/2) * base * altitude.
Substituting the given values into the formula, we have:
162 = (1/2) * b * h
Since b = 4h, we can substitute it into the equation:
162 = (1/2) * 4h * h
Simplifying this equation, we get:
162 = 2h^2
Divide both sides of the equation by 2:
81 = h^2
To solve for h, we take the square root of both sides:
√81 = √h^2
Since we are dealing with length, the square root will give us the positive value:
9 = h
Therefore, the altitude of the triangle is 9 cm.