A cabinet door has a perimeter of 62 inches its area is 228 in.² what are the dimensions of the door

P=2 (L+W)

A=LW

given

P=62

62=2 (L+W)

divide 2

31=L+W

minus W

L=31-W

sub into other one

A=LW

A = (31-W) (W)

228=31W-W^2

times - 1

W^2-31W=-228

add 228 both sides

W^2-31W+228=0

factor

what 2 numbers multiply to get 228 and add to get - 31

-19 and - 12

(W-19) (W-12) = 0

set to zero

W-19=0

W=19

W-12=0

W=12

sub back

L=31-W

L=31-12

L=19

or

L=31-19

L=12

the doorway is 12in by 19in