For a triangle with sides 12 and 15, heights are drawn to these sides, the height drawn

For a triangle with sides 12 and 15, heights are drawn to these sides, the height drawn to the first side is 10, find the length of the height drawn to the second height.

The formula for calculating the area of a triangle:

S = (a × h) / 2, where a is the length of the side of the triangle, h is the length of the height of the triangle dropped to side a.

Let us denote the required side by x.

We get:

S = (12 × 10) / 2.

Also S = (15 × x) / 2.

Let’s equate the obtained expressions and solve the equation:

(12 × 10) / 2 = (15 × x) / 2;

120 = 15 x x;

x = 8.

Answer: the length of the height drawn to the second side is 8.