Hey there!!
What is the area of a rectangle?
The area of a rectangle = Length × Breadth
Given :
Length is 6m longer than the width.
Hence, length = 6 + breadth
Area = ( 6 + breadth ) ( breadth )
Area = 6 breadth + breadth²
Area = 775
Hence, 775 = 6 breadth + breadth²
( Let's take the breadth as ' b ' )
775 = 6b + b²
... b² + 6b - 775 = 0
... b² - 25b + 31b - 775 = 0
... b ( b - 25 ) + 31 ( b - 25 ) = 0
... ( b + 31 ) ( b -25 ) = 0
There are two solutions found :
b + 31 = 0 and b - 25 = 0
Hence,
b = -31 and b = 25
As the values can not be in negatives, we take 25
Hence, the value of the breadth is 25.
Length = 6 + b
Length = 31
Hence, the value of the length = 31
Hope my answer helps!!