KVPY Sample Paper KVPY Stream-SX Model Paper-1

The sides of a right angled triangle are in arithmetic progression. If the triangle has area 24. Then, the length of smallest side is

A) 6

B) 8

C) 10

D) 12

Correct Answer: A

Solution :

[a]

Let the side of right angled triangle are \[a-d,\]\[a,a+d.\]
\[\therefore \]\[{{(a-d)}^{2}}+{{a}^{2}}={{(a+d)}^{2}}\]
\[\Rightarrow \] \[{{a}^{2}}={{(a+d)}^{2}}-{{(a-d)}^{2}}\]
\[\Rightarrow \] \[{{a}^{2}}=4ad\]
\[\Rightarrow \] \[a=4d\]	? (i)
Area of triangle \[=\frac{1}{2}a\,(a-d)=24\]
\[\Rightarrow \]\[a\,(a-d)=48\]	? (ii)
From Eqs. (i) and (ii) we get
\[a=8,\,\,d=2\]
\[\because \]Smallest side is \[a-d=8-2=6\]