Question

If the perimeter and area of ​​a rectangular garden is 138 meters 1178 square meters respectively, what is the difference between the length and width of the garden?​

Answer 1

Step-by-step explanation:

2(l+b)=138 ( perimeter of rectangle)

l×b = 1178

( l + b ) ^2 = ( 69)^2 ( l + b = 138÷ 2 => 69 )

l^2 + b ^2 + 2lb = 4761 ( 69^2)

l^2 + b^2 + 2( 1178 ) = 4761

l^2 + b^2 + 2356 = 4761

l^2 + b^2 = 2405 ( 4761 - 2356 )

l^2 + b^2 can be written as ( l - b ) ^2 + 2lb if we expand it we get l^2 + b^ 2

( l - b ) ^2 + 2lb = 2405

( l - b ) ^ 2 + 2( 1178 ) = 2405

( l - b ) ^ 2 = 2405 - 2356

( l - b ) ^ 2 = 49

( l - b ) = under root of 49 i.e., + or - 7

Area won't be negative so answer is + 7