Question

Consider the given rectangle with heightequals4timeswidth. Let x be the width of the rectangle. Write an expression for the​ perimeter, P. If the area is 49 square​ feet, write this fact as an equation.

Answer 1

Answer:

The expression for the perimeter P is $P=\frac{784+h^2}{2h}$ feet.

Area=49=lx square feet ( here $x=\frac{h}{4}$ )

Step-by-step explanation:

Given that rectangle with height equals 4times width.

It can be written as

$h=4\times width$

Let x be the width of the given rectangle

Therefore $h=4\times x$

$h=4x$

$\frac{h}{4}=x$

Rewritting the above equation we get

$x=\frac{h}{4}$

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=$x=\frac{h}{4}$ )

Rewritting we get

lx=49 square feet.

$l=\frac{49}{x}$

$=\frac{49}{\frac{h}{4}}$

$l=\frac{49\times 4}{h}$

$l=\frac{196}{h}$ feet

Perimeter P$=2(l+w)$ units

$P=2(\frac{196}{h}+\frac{h}{4})$

$P=\frac{2(196)}{h}+\frac{2(h)}{4}$

$=\frac{392}{h}+\frac{h}{2}$

$=\frac{392(2)+h^2}{2h}$

$P=\frac{784+h^2}{2h}$ feet.