Question

In right triangle ABC, altitude CD is drawn to hypotenuse AB. If AD equals 4 and AC exceeds DB by 1, find DB.

It is from a worksheet about proportions in a right triangle.

Answer 1

I assume you made a diagram, or were given one.
Angle C should be 90

let BD = x
then AC = x+1

I see three similar triangles, but the important one is
ADC similar to
ACB

then AD/AC = AC/AB

4/(x+1) = (x+1)/(x+4) which turns into
x^2 - 2x - 15 = 0
(x-5)(x+3) = 0
x = 5 or x = -3, but clearly x > 0
so x = 5

BD = 5