You are building a new wooden deck on your house. The old deck had a length of (2x + 1) feet and a width of (3x – 3) feet. You want to make it bigger, so you are going to add x feet to the width. The area of the new deck will be 493 square feet. What is the length and width of the new deck? HELPPP

suggestions algebra calculator or math

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

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step-by-step explanation:

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