Question

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

Answer 1

Length= 17 feet

Width= 29 feet

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