Hello, Vitamin!

Let = length of "one leg"One leg of a right triangle is 24.0 cm longer than the other leg.

If the hyptoenuse is to be greater than 65.0 cm,

what values for the length of the other leg are permissible?

Let = length of "other leg".

Then we have: .

. . which simplifies to: .

This is an up-opening parabola which is negative between its x-intercepts

. . and positive "outside" its x-intercepts.

For its x-intercepts: .

. . Quadratic Formula: .

The roots are: .

Therefore: .