Answer:
The width is 7 feet and length is 18 feet
Step-by-step explanation:
Let length of rectangle be "l" and width of rectangle be "w"
The area of a rectangle is length * width
Area is given as 126, so we can write:
[tex]lw=126[/tex]
Also, given length is 4 feet longer than TWICE width, so we can write:
l = 4 + 2w
We replace first equation with this equation and simplify to get:
[tex]lw=126\\(4+2w)(w)=126\\4w+2w^2=126\\2w^2+4w-126=0\\w^2+2w-63=0[/tex]
We can do middle term factorization and find the value(s) of w:
[tex]w^2+2w-63=0\\(w+9)(w-7)=0\\w=-9,7[/tex]
Width CANNOT be negative, so we take w = 7
Now, finding l:
l = 4 + 2w
l = 4 + 2(7)
l = 4 + 14
l = 18
The width is 7 feet and length is 18 feet
