Atriangle that has 13-inch side, a 14-inch side, and a 15-inch side has an area o 84 square inches? how can i find the lengths of all three altitudes of this triangle

The answer is 12.92 in, 12 in, and 11.2 in

The area (A) of the triangle is:
A = s * a / 2
s - side
a - altitude

We know:
A = 84 in²
s1 = 13 in
s2 = 14 in
s3 = 15 in
a1 = ?
a2 = ?
a3 = ?


a1 = ?
A = s1 * a1 / 2
84 = 13 * a1 / 2
84 * 2 = 13 * a1
168 = 13 * a1
a1 = 168 / 13
a1 = 12.92 in


a2 = ?
A = s2 * a2 / 2
84 = 14 * a2 / 2
84 * 2 = 14 * a2
168 = 14 * a2
a2 = 168 / 14
a2 = 12 in


a3 = ?
A = s3 * a3 / 2
84 = 15 * a3 / 2
84 * 2 = 15 * a3
168 = 15 * a3
a3 = 168 / 15
a3 = 11.2 in