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

The expression for the perimeter P is
`P=(784+h^2)/(2h)` feet.

Area=49=lx square feet ( here
`x=(h)/(4)` )

Explanation:

Given that rectangle with height equals 4times width.

It can be written as

`h=4* width`

Let x be the width of the given rectangle

Therefore
`h=4* x`

`h=4x`

`(h)/(4)=x`

Rewritting the above equation we get

`x=(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=(h)/(4)` )

Rewritting we get

lx=49 square feet.

`l=(49)/(x)`

`=(49)/((h)/(4))`

`l=(49* 4)/(h)`

`l=(196)/(h)` feet

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

`P=2((196)/(h)+(h)/(4))`

`P=(2(196))/(h)+(2(h))/(4)`

`=(392)/(h)+(h)/(2)`

`=(392(2)+h^2)/(2h)`

`P=(784+h^2)/(2h)` feet.