RRB Assistant Loco Pilot and Technician Model Paper 1 with solutions

(c) Smallest side of the triangle = x cm (let)
Second side of triangle
= 40 – 17 – x = 23 – x
Semi perimeter = s = 40/2 =20
∴ $\sqrt{\mathrm{s}\left(\mathrm{s}-\mathrm{a}\right)\left(\mathrm{s}-\mathrm{b}\right)\left(\mathrm{s}-\mathrm{c}\right)}$ = 60
⇒ (20 – x) (x – 3) = 60
⇒ 20x – 60 – ${\mathrm{x}}^2$ + 3x = 60
⇒${\mathrm{x}}^2$ – 23x + 120 = 0
⇒${\mathrm{x}}^2$ – 15x – 8x + 120 = 0
⇒ x (x – 15) – 8 (x – 15) = 0
⇒(x – 8) (x – 15) = 0
⇒ x = 8 or 15