JEE Advanced 2017 · Paper 1 · Mathematics Q12

MathematicsInteger+3Question 48 of 54

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

Your answer

Answer and worked solution

Official answer: 6

Set up. Take sides $a-d$ , $a$ , $a+d$ :
$(a-d)^2+a^2=(a+d)^2\implies a^2=4ad\implies a=4d.$
The sides are $3d$ , $4d$ , $5d$ .

Area. $\tfrac12(3d)(4d)=6d^2=24$ , so $d=2$ . The smallest side is $3d=6$ .

Answer: 6

Topics:Arithmetic progression

JEE Advanced 2017 · Paper 1, Mathematics question 12