PYQ
Question | āĻĒā§ā§°āĻļā§āĻ¨ : The perimeter of a rhombus is 100 m and one diagonal is 14 m. Find the other diagonal. āĻāĻāĻž āĻ¸āĻŽāĻāĻ¤ā§ā§°ā§āĻā§āĻā§° āĻĒā§°āĻŋāĻ¸ā§āĻŽāĻž 100 āĻŽāĻŋāĻāĻžā§° āĻā§°ā§ āĻāĻāĻž āĻā§°ā§āĻŖ 14 āĻŽāĻŋāĻāĻžā§°āĨ¤ āĻāĻ¨āĻā§ āĻā§°ā§āĻŖā§° āĻĻā§ā§°ā§āĻā§āĻ¯ āĻ¨āĻŋā§°ā§āĻŖāĻ¯āĻŧ āĻā§°āĻāĨ¤
A. 48 m B. 42 m C. 50 m D. 40 m
Solution | āĻ¸āĻŽāĻžāĻ§āĻžāĻ¨
Perimeter = 100 m ⇒ Side = 100 ÷ 4 = 25 m (āĻĒā§°āĻŋāĻ¸ā§āĻŽāĻž = 100 āĻŽāĻŋāĻāĻžā§° ⇒ āĻŦāĻžāĻšā§ = 100 ÷ 4 = 25 āĻŽāĻŋāĻāĻžā§°)
Half of the given diagonal (āĻĻāĻŋāĻ¯āĻŧāĻž āĻā§°ā§āĻŖā§° āĻāĻ§āĻž)= 14 ÷ 2 = 7 m (āĻŽāĻŋāĻāĻžā§°)
Using Pythagoras' Theorem : āĻĒāĻžāĻāĻĨāĻžāĻā§ā§°āĻžāĻā§° āĻāĻĒāĻĒāĻžāĻĻā§āĻ¯ āĻŦā§āĻ¯ā§ąāĻšāĻžā§° āĻā§°āĻŋ:
252 = 72 + (d/2â)2
625 = 49 + (d/2)2
(d/2)2 â= 576
d/2 = 24
d = 48m
Ans | āĻāĻ¤ā§āĻ¤ā§°: A. 48 m
Trick | āĻā§ā§°āĻŋāĻ : Perimeter ÷ 4 → Side → Half of the given diagonal → Pythagoras → Pythagoras → ×2 (āĻŦāĻžāĻšā§ = āĻĒā§°āĻŋāĻ¸ā§āĻŽāĻž ÷ 4 → āĻā§°ā§āĻŖā§° āĻāĻ§āĻž → āĻĒāĻžāĻāĻĨāĻžāĻā§ā§°āĻžāĻ → ×2)