Respuesta :
Answer:
Dimension= [tex](4\times 7)\ feet[/tex]
Step-by-step explanation:
Given: Area of Carport= 28 feet²
The height of the carport is 1 feet less than 2 times its length.
Lets assume the length of Carport be "w"
∴ Height of carport= [tex](2w-1)\ feet[/tex]
We know, Area of rectangle= [tex]width\times length[/tex]
∴[tex]28= w\times (2w-1)[/tex]
Using distributive property of multiplication.
⇒ [tex]28= 2w^{2} -w[/tex]
Subtracting both side by 28.
⇒ [tex]2w^{2} -w-28= 0[/tex]
Using the quadratic formula to solve the equation.
⇒ [tex]2w^{2} -w-28= 0[/tex]. what are the values of w.
Solving by using quadratic formula.
Formula: [tex]\frac{-b\pm \sqrt{b^{2}-4(ac) } }{2a}[/tex]
∴ In the equation [tex]2w^{2} -w-28= 0[/tex] , we have a= 2, b= -1 and c= -28.
Now, subtituting the value in the formula.
= [tex]\frac{-(-1)\pm \sqrt{(-1)^{2}-4(2\times -28) } }{2\times 2}[/tex]
= [tex]\frac{1\pm \sqrt{1 - 4(-56) } }{4}[/tex]
Opening parenthesis.
= [tex]\frac{1\pm \sqrt{1+224 } }{4}[/tex]
= [tex]\frac{1\pm \sqrt{225}}{4}[/tex]
We know 15²=225
= [tex]\frac{1\pm \sqrt{15^{2}}}{4}[/tex]
we know √a²=a
= [tex]\frac{1\pm 15 }{4}[/tex]
Now we have two solution
= [tex]\frac{16}{4} \ or\ \frac{-14}{4}[/tex]
Ignoring negative base or width or carport
∴ w= [tex]\frac{16}{4} = 4[/tex]
Hence, Length of carport is 4 feet
next subtituting the value of length to get height of carport
Height of carport= [tex](2w-1)\ feet[/tex]
⇒ Height of carport= [tex](2\times 4-1)[/tex]
⇒ Height of carport= [tex]7\ feet[/tex]
Hence dimension of rectangular carport= [tex](4\times 7)\ feet[/tex]
