Question

If the sides of a right triangle are in AP then the ratio of smallest side to the greatest side is-

Answer 1

Answer:

3 : 5

Step-by-step explanation:

if sides in AP,

Sides are a-d, a, a+d,

moreover it is a right angled triangle,

so,

(a-d)^2 + a^2 = (a+d)^2

=>a^2 - 2ad + d^2 + a^2 = a^2 + 2ad + d^2

cancelling a^2, d^2,

a^2 - 2ad = 2ad

a^2 = 4ad

a = 4d

ratio of smallest and greatest is,

4d - d : 4d + d

3d : 5d

3 : 5