A person wishes to fence 375m2 rectangular garden. He has 65m of barbed wire and is able to fence only three sides of the garden. What is the perimeter of the garden?
Given, Area of rectangular garden =375m2‌‌...‌ (i) ‌ Sum of the lengths of three sides of garden =65m... (ii) Let length and breadth of the garden be x and ym.
Then, x×y‌‌=375m2‌[‌ from Eq. (i) ‌]...‌ (iii) ‌ x+y+x‌‌=65‌[‌ from Eq. (ii)] ‌ ⇒2x+y‌‌=65‌ ⇒‌‌y‌‌y‌‌=65−2x‌...‌ (iv) ‌ From Eq. (iv), put y=65−2x into Eq. (iii), we get ‌x⋅(65−2x)=375 ⇒‌65x−2x2=375 ⇒‌2x2−65x+375‌‌=0 ⇒‌2x2−50x−15x+375‌‌=0 ⇒‌2x(x−25)−15(x−25)‌‌=0 ⇒‌‌(x−25)‌(2x−15)‌‌=0 ⇒‌x‌‌=25‌ or ‌‌