Respuesta :
Answer:
The expression for the perimeter P is [tex]P=\frac{784+h^2}{2h}[/tex] feet.
Area=49=lx square feet ( here [tex]x=\frac{h}{4}[/tex] )
Step-by-step explanation:
Given that rectangle with height equals 4times width.
It can be written as
[tex]h=4\times width[/tex]
Let x be the width of the given rectangle
Therefore [tex]h=4\times x[/tex]
[tex]h=4x[/tex]
[tex]\frac{h}{4}=x[/tex]
Rewritting the above equation we get
[tex]x=\frac{h}{4}[/tex]
To write an expression for the perimeter P of the given rectangle :
Also given that area of the rectangle is 49 square feet.
Area=49 square feet.
We know area of rectangle = lw square units.
Therefore area=49=lx square feet ( here area=49 and w=[tex]x=\frac{h}{4}[/tex] )
Rewritting we get
lx=49 square feet.
[tex]l=\frac{49}{x}[/tex]
[tex]=\frac{49}{\frac{h}{4}}[/tex]
[tex]l=\frac{49\times 4}{h}[/tex]
[tex]l=\frac{196}{h}[/tex] feet
Perimeter P[tex]=2(l+w)[/tex] units
[tex]P=2(\frac{196}{h}+\frac{h}{4})[/tex]
[tex]P=\frac{2(196)}{h}+\frac{2(h)}{4}[/tex]
[tex]=\frac{392}{h}+\frac{h}{2}[/tex]
[tex]=\frac{392(2)+h^2}{2h}[/tex]
