How do you find the dimensions of a rectangle if the area is 63cm^2 and the perimeter is 32cm where x represents the width of the rectangle?

1 Answer

Width = 7cm; Length = 9cm

Explanation:

let color(red)x be the width and color(red)y be the length of the rectangle.

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Given
area = x*y = 63 -----------(1)

perimeter =x+y+x+y = 2x+2y = 32 ----------(2)

from (1), x=63/y

substituting this in (2),

63/y+y=16

=>y^2-16y+63=0

=> y^2-7*y-9*y+63=0

=>y(y-7)-9(y-7)=0

=>(y-9)(y-7)=0

=> either y-9=0 i.e. y=9

or y-7=0 i.e. y=7

therefore x=63/9=7 or x=63/7=9

Hence, width = 7cm; length = 9cm