Answer:
Length= 17 feet
Width= 29 feet
Step-by-step explanation:
Original
Length= (2x +1) ft
Width= (3x -3) ft
New deck
Length= (2x +1) ft
Width
= (3x -3 +x) ft
= (4x -3) ft
Area of deck= length ×width
493= (2x +1)(4x -3)
Expand:
493= 2x(4x) +2x(-3) +1(4x) +1(-3)
493= 8x² -6x +4x -3
493= 8x² -2x -3
8x² -2x -3 -493= 0
8x² -2x -496= 0
Divide by 2 throughout:
4x² -x -248= 0
Factorise:
(x -8)(4x +31)= 0
x -8=0 or 4x +31= 0
x= 8 or 4x= -31 (reject)
Length of new deck
= 2(8) +1
= 16 +1
= 17 ft
Width of new deck
= 4(8) -3
= 32 -3
= 29 ft
