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Question

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


Solution

Let the sides are a - d, a and a + d. Then,
a (a - d) = 48 sq. units   (from eqn. of area of triangle)
and (ad)2+a2=(a+d)2       . . .(Pythagoras)
a22ad+d2+a2=a2+2ad+d2
a2=4ad
a=4d
Thus, a=8, d=2
Hence, ad=6 units

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