### The sides of a triangle are 13 cm, 37 cm and 40 cm. The altitude to the longest side is:

12 cm

Step by Step Explanation:
1. Let's assume the altitude to the longest side be 'h'.
The following picture shows the required triangle,

The area of the triangle ΔABC can be calculated using Heron's formula since all sides of the triangles are known.
S =
 AB + BC + CA 2

=
 40 + 37 + 13 2

= 45 cm.
The area of the ΔABC = √S(S - AB)(S - BC)(S - CA)
= √45(45 - 40)(45 - 37)(45 - 13)
= 240 cm2
2. The altitude to the longest side =
 2 × (The area of the ΔABC) Base 'AB'

=
 2 × 240 40

= 12 cm.

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