Two sides of a triangle are 8cm and 12cm long, and the altitude to the 8-cm side is 9cm. How long is the altitude to the 12-cm side?
We can find the area
area = (1/2)(8)(9) = 36
area using the other altitude = (1/2)(h)(12) = 6h
but the area must stay the same:
6h = 36
h = 6
If three sides of a triangle are 8cm,9cm and 12cm calculate the perimeter of the triangle
To find the length of the altitude to the 12-cm side of the triangle, we can use the formula for the area of a triangle. The formula is:
Area = (1/2) * base * height
In this case, the base is the 12-cm side, and the height is the altitude to the 12-cm side. We can rearrange the formula to solve for the height:
height = (2 * Area) / base
First, let's find the area of the triangle. To do this, we can use the fact that the area of a triangle is equal to the product of the base and height, divided by 2. In this case, the base is 12 cm and the height is 9 cm:
Area = (1/2) * 12 cm * 9 cm
= 54 cm²
Now, we can substitute the values into the formula for height:
height = (2 * Area) / base
= (2 * 54 cm²) / 12 cm
= 108 cm² / 12 cm
= 9 cm
Therefore, the length of the altitude to the 12-cm side is 9 cm.