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 (a−d)2+a2=(a+d)2       . . .(Pythagoras) ⇒a2−2ad+d2+a2=a2+2ad+d2 ⇒a2=4ad ⇒a=4d Thus, a=8, d=2 Hence, a−d=6 units

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