Question

the sides of a right angled triangle are in arithmetic progression. if the triangle has area 24 then what is the length of the smallest side. ​

Answer 1

$\bf \huge \mathfrak \orange{answer : }$

$\bf \huge \red{6}$

STEP-BY-STEP VERIFICATION:

Let the sides be a-d, a , a+d

Then (a-d)^2 + a^2=(a+d)^2 by Pythagoras theorum.

Also a(a-d)/2=24

Solve these 2 equations to get a and d

a will be 8 and d will be 2

Smallest side will be a-d=8–2=6

Answer 2

Hey mate,.

Let the sides be a – d, a, a + d where d is positive.

Using Pythagoras theorem,

(a + d)2 = (a – d)2 + a2 => a = 4d

∴ Sides are 3d, 4d, 5d

Area = 24 => 1/2 x 3d x 4d

= 24 => d = 2

∴ Sides are 6, 8, 10.

∴ Smallest side = 6

Hope it will help you