The sides of a right angled triangle are in arithmetic progression .If the triangle has aera 24, then what is the length of its smallest side ?

Options

A. 3
B. 6
C. 4
D. 8

Answer

B

Explanation

Let the lengths of the sides of the triangle be `a-d,a,a+d,dgt0`. Clearly, a+d is the largest side i.e. the hypotenuse of the triangle.
`:." "(a+d)^(2)=(a-d)^(2)+a^(2)rArra=4d`.
So, the length of the sides are 3d, 4d, 5d.
It is given that the area of the triangle is 24 sq. units.
`:." "(1)/(2)(3d xx 4d)=24rArrd=2`
So, the length of the sides are : 6,8,10.
Hence, the length o the smallest side is 6.