If the sides of a disheveled triangle is 9cm, 9cm and 4cm, find the height on the shortest side.
What is a disheveled triangle?
Sorry, I mean a isosceles triangle
To find the height on the shortest side of a triangle, we can use the formula:
Area = 0.5 * base * height
In this case, the shortest side of the triangle is 4cm. To find the height, we need to know the length of the base - the side to which the height is drawn. Let's assume the base is the side with length 9cm.
Now, let's calculate the area of the triangle using Heron's formula:
First, calculate the semi-perimeter (s) using the formula:
s = (a + b + c) / 2
where a, b, and c are the lengths of the triangle's sides.
In this case, a = 9cm, b = 9cm, and c = 4cm:
s = (9cm + 9cm + 4cm) / 2
s = 22cm / 2
s = 11cm
Next, we can calculate the area (A) of the triangle using Heron's formula:
A = sqrt(s * (s - a) * (s - b) * (s - c))
A = sqrt(11cm * (11cm - 9cm) * (11cm - 9cm) * (11cm - 4cm))
A = sqrt(11cm * 2cm * 2cm * 7cm)
A = sqrt(308cm^2)
A ≈ 17.55cm^2 (rounded to two decimal places)
Finally, we can find the height (h) on the shortest side using the formula:
Area = 0.5 * base * height
17.55cm^2 = 0.5 * 4cm * h
Solve for h:
h = (2 * 17.55cm^2) / 4cm
h ≈ 8.78cm (rounded to two decimal places)
Therefore, the height on the shortest side (base) of the disheveled triangle is approximately 8.78cm.