A triangle with sides 15 and 5 has heights to these sides. the height drawn to the first side is 1.

A triangle with sides 15 and 5 has heights to these sides. the height drawn to the first side is 1. What is the height drawn to the second side?

The area of the triangle is:

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 height length as x.

We get:

S = (15 × 1) / 2.

Also S = (5 × x) / 2.

We equate the obtained expressions and solve the equation:

(15 × 1) / 2 = (5 × x) / 2;

15 = 5 × x;

x = 3.

Answer: The length of the height drawn to the second side is 3.