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 w ant 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?
2 answers:
Answer:
Length= 17 feet
Width= 29 feet
Step-by-step explanation:
<u>Original</u>
Length= (2x +1) ft
Width= (3x -3) ft
<u>New deck</u>
Length= (2x +1) ft
Width
= (3x -3 +x) ft
= (4x -3) ft
Area of deck= length ×width
493= (2x +1)(4x -3)
<em>Expand</em><em>:</em>
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
<em>Divide</em><em> </em><em>by</em><em> </em><em>2</em><em> </em><em>throughout</em><em>:</em>
4x² -x -248= 0
<em>Factorise</em><em>:</em>
(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
Answer:
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