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.
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.
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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
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