Question

Roy has a patio that covers 434 ft ^2. He wants to increase his patio 196 ft ^2 by adding 4 ft to both the length and width. The length of the original patio is 3 ft more than twice the width. What is the length of the new patio

Answer 1

First, Area=Length*Width

Original Length=3+2*Width
434=Original Length*Original Width
434=(3+2*Width)*Width
434=3*Width+2*Width^2
I solved by graphing, you can do another way if you want.

Width is 14 ft. Original Length is 31 ft.

Add 4 and you get the answer: 35 feet

Answer 2

Ty!

Answer 3

Algebraic way:

original width = x
original length = 2x+3

x(2x+3) = 434
2x^2 + 3x - 434 = 0
(x - 14)(2x + 31) = 0
x = 14 or x = -31/2 , which I will reject

original width is 14 ft
original length is 31 ft

new width = 18
new length = 35